Book Description
The theory of $J$-holomorphic curves has been of great importance since its introduction by Gromov in 1985. Its mathematical applications include many key results in symplectic topology. It was also one of the main inspirations for the creation of Floer homology. In mathematical physics, it provides a natural context in which to define Gromov-Witten invariants and quantum cohomology--two important ingredients of the mirror symmetry conjecture.
This book establishes the fundamental theorems of the subject in full and rigorous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associativity of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology: There are two long chapters on applications, one concentrating on classical results in symplectic topology and the other concerned with quantum cohomology. The last chapter sketches some recent developments in Floer theory. The five appendices of the book provide necessary background related to the classical theory of linear elliptic operators, Fredholm theory, Sobolev spaces, as well as a discussion of the moduli space of genus zero stable curves and a proof of the positivity of intersections of $J$-holomorphic curves in four dimensional manifolds.
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Riemannian Geometry of Contact and Symplectic Manifolds
David E. Blair , and
D.E. Blair
Manufacturer: Birkhäuser Boston
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ASIN: 0817642617 |
Book Description
This monograph deals with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter. The text is carefully presented. Topics unfold systematically from Chapter 1, which examines the general theory of symplectic manifolds. Principal circle bundles (Chapter 2) are then discussed as a prelude to the Boothby--Wang fibration of a compact regular contact manifold in Chapter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on the general setting of Riemannian metrics associated with both symplectic and contact structures, and Chapter 5 is devoted to integral submanifolds of the contact subbundle. Topics treated in the subsequent chapters include Sasakian manifolds, the important study of the curvature of contact metric manifolds, submanifold theory in both the K¿hler and Sasakian settings, tangent sphere bundles, curvature functionals, complex contact manifolds and 3 Sasakian manifolds. The book serves both as a general reference for mathematicians to the basic properties of symplectic and contact manifolds and as an excellent resource for graduate students and researchers in the Riemannian geometric arena. The prerequisite for this text is a basic course in Riemannian geometry.
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Contact and Symplectic Geometry (Publications of the Newton Institute)
Manufacturer: Cambridge University Press
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ASIN: 0521570867 |
Book Description
This volume presents a mix of substantial expository articles and research papers that outline important and topical ideas in the area of contact and symplectic geometry. Many of the results have not been presented before, and the lectures on Floer homology are the first available in book form. Symplectic methods are one of the most active areas of research in mathematics currently, and this volume will attract much attention among professional mathematicians.
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Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology (NATO Science Series II: Mathematics, Physics and Chemistry)
Manufacturer: Springer
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ASIN: 1402042736 |
Book Description
This volume contains contributions to the Séminaire de Mathématiques Supérieures – NATO Advanced Study Institute on "Morse theoretic Methods in non-linear Analysis and Symplectic Topology" which was held at the Université de Montréal in the summer of 2004.
The recent years have witnessed the emergence of a deeper and more general formalism of the main geometric ideas in these fields. The surveys and research papers in this volume are a striking example of this trend. They provide an up-to-date overview of some of the most significant advances in these topics. The text is of high relevance for graduate students as well as for more senior mathematicians with interest in a wide range of topics going from symplectic topology to dynamical systems and from algebraic and differential topology to variational methods.
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Symplectic and Contact Topology: Interactions and Perspectives (Fields Institute Communications, V. 35)
Manufacturer: American Mathematical Society
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ASIN: 0821831623 |
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Symplectic Geometry of Integrable Hamiltonian Systems (Advanced Courses in Mathematics - CRM Barcelona)
Michèle Audin ,
Ana Cannas da Silva , and
Eugene Lerman
Manufacturer: Birkhäuser Basel
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ASIN: 3764321679 |
Book Description
Among all the Hamiltonian systems, the
integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book).
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Geometrie symplectique et de contact: Journees lyonnaises de la Societe mathematique de France, 14-17 juin 1983 (Seminaire sud-rhodanien de geometrie)
Manufacturer: Hermann
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ASIN: 2705659714 |
Book Description
The Private Memoirs and Confessions of a Justified Sinner is a startling tale of murder and madness set in a time of troubles like our own. Robert Wringhim is a religious fanatic: one of God's chosen who believes himself free to disregard the strictures of morality—a view in which he is much encouraged by the elusive, peculiarly striking foreigner who becomes his dearest friend. Describing the seductive mutual dependence of these soulmates and the way—efficient at first, then increasingly intoxicated—they go about settling scores with their (and of course God's) enemies, James Hogg presents a powerful picture of evil in the world and in the heart and mind. This work of black humor, acute psychological insight, and, in the end, deeply compassionate humanity is one of the masterpieces of literature in English.
Customer Reviews:
THis book is awesome. .......2007-07-31
I loved the comedic narrative that starts off the book; it's a colorful and richly detailed black comedy that youd expect from HAWTHORN- making fun of the clash between overly zealous religious funamentalists and more earthy rural folk. As the story progresses it decends into a dramatic/tragic tone that I would compare to CHARLES BROCKDON BROWN.
then the story breaks into the second part.
THe change to the killers perspective/narrative is a huge unexpected leap that I would have to compare to RASHOMON. It describes many of the same events with such a dramatic shift of emphasis that you almost do not recognize the scenes. Some of the multi perspective breaks are funny, some are chilling.
THis killers perspective is brilliant; he's a realistically depicted schizophrenic serial killer that filters his agression through religious delusion. It reminds me of the movie NIGHT OF THE HUNTER, mixed with KILLER INSIDE ME. He also has a DR JEKYLE MR HYDE split personality that reminds me of FIGHT CLUB.
I have experience with schizos and have had the joy of being targeted by a psychopath... the realistic portrayal of mental illness in this book is impressive.
Doppleganger.......2007-03-16
Is Robert a schizophrenic to be pitied or a psychopath to be loathed?
Similar to Dostoyevsky's psychodrama, The Double, we find the exhileration of the psyche brought bare before our perusal. James Hogg's two part account of a "sinner" (a predestined and chosen one albeit) is on surface a derisive gothic narrative of the Calvinistic doctrine of predestination. The taut trance-like animated lustre it creates is exceptionally haunting. The author succeeds in invoking the sublime and supernatural within the fragile make-up of a psyche twisted and enlightened by the religious zeal it professes. If Percy Shelley found the tale as insightful as any upopn the workings of the mind it was primarily because of the tenacity of the precepts which justify the sinner's actions and provoke his behavior. A landscape of horrific charge stages a mind terrifying and a depth where foundations are dug to the root and these dragged with a vengence upon the highest peaks of a reprobates mind. Similar to the Marquis De Sade - studies on sexual allusions between the protagonist and the devil are amusing and should be dabbled into - in its use of reason to legitimize otherwise deplorable executions of conscience; this narrative strikes a balance between two accounts of the same fratricide and ensuing murders, where we are left dizzy and confused and thrown into a state of mind persecuted by truth and the mind's ability to obviate the most simple excesses as they are practiced and divined. At times we question the existence of the double, and on other occasions we are in awe of his personality and presence. The second account is of greater psychological depth and makes one confide with the mind of a murderer propelled by his faith. However we cannot but continue to query our sensibility imputing greed and a rationalizing tendency at play. The author's ambiguity make for rewarding continued readings for this is indeed a psychological analysis of exceptional powers.
Beautiful and unbelievable, wonderful and frightening. A pleasure to read and a wonder to study.
Of related study is Anthony Burgess' Enderby Trilogy, where the novel and Hogg are assimilated; the execution of the novel is very much in tune with the madness of James Hogg's Confessions of a Justified Sinner.
Synopsis: A supernatural psychological thriller.......2007-02-08
The story of James Hogg's "Private Memoirs and Confessions of a Justified Sinner" describes events 100 years before Hogg's own lifetime, and revolves around Robert Wringhim, a young man with a questionable paternal origin, and confused religious principles. His mother and her husband George Colwan have fathered his older half-brother George, but Robert appears to be the product of his mother's unchastity with the fanatic Revd Robert Wringhim. This minister becomes his surrogate father and mentor, and begins instilling in young Robert the conviction that those who are predestined to eternal life cannot sin, and that the reprobate are to be despised: "To the wicked all things are wicked; but to the just, all things are just and right ... How delightful to think that a justified person can do no wrong."(p9) The first third of the book purports to be an unnamed editor's narrative, recounting the conflict between the two brothers, and the eventual murder of George under dubious and mysterious circumstances.
The mystery is uncovered in the remainder of the book, which contains the alleged first-hand account of young Robert's memoirs and confessions. (Warning: plot spoilers ahead) Here Hogg excels in painting a dark and supernatural portrait of the mind of Robert, as he is overcome by demonic powers. His father's teaching becomes the breeding ground for his twisted theology. Initially Robert is fearful of unchangeable rejection by God: "I lived in a hopeless and deplorable state of mind; for I said to myself, `If my name is not written in the book of life from all eternity, it is in vain for me to presume that either vows or prayers of mine, or those of all mankind combined, can ever procure its insertion now.'" (p69) Finally Robert's father claims to have received secret revelation giving assurance of election: "he embraced me, and welcomed me into the community of the just upon earth." The assurance of acceptance by God is understood by Robert to mean "that I was now a justified person, adopted among the number of God's children - my name written in the Lamb's book of life, and that no by-past transgression, nor any future act of my own, or of other men, could be instrumental in altering the decree." (p79)
From this point Robert's memoirs become "a relation of great and terrible actions, done in the might, and by the commission of heaven." (p.79) Under the tutelage of his father, Robert's mind is already open to religious bigotry: "Seeing that God had from all eternity decided the fate of every individual that was to be born of woman, how was it in man to endeavour to save those whom their Maker had, by an unchangeable decree, doomed to destruction." (p.85) His antinomian thinking is nurtured and encouraged by a mysterious nameless companion who enters Robert's life, and becomes his mentor and friend, and encourages Robert's notion that as one of the righteous his divinely-appointed mission and task is to destroy the wicked with the sword. The things that Robert's companion "strove most to inculcate on my mind were the infallibility of the elect, and the preordination of all things that come to pass."(p87).
Although Robert perceives his companion to be a great prince with many subjects, possibly even the Czar of Russia, it gradually becomes clear that it is in fact an incarnation of the Prince of Darkness, Satan, disguised as an angel of light. (A common interpretation that it is purely psychological figment of Robert's imagination, possibly even a multiple personality, is impossible because several individuals in the novel witness him as a physical presence alongside Robert, so clearly he exists outside Robert's mind.) Robert initially seems to question the fact that Gil-Martin - the name the mysterious stranger eventually gives himself - has the unearthly ability to take appearances of others, and that he refuses to pray (p88). His corrupting influence over Robert's mind increases, until Robert finds that he is unable to account for large amounts of time, and where he is accused of doing things about which he knows nothing. Slowly he becomes cognitive of the fact that Gil-Martin not only can present himself as another person (even Robert himself), but at times controls Robert totally by entering him. Robert first suggests that he has "two souls, which take possession of my bodily frame by turns" (p132) but Gil-Martin eventually presents the truth: "I am wedded to you so closely that I feel as if I were the same person. Our essences are one, our bodies and spirits being united ... and, wherever you are, there must my presence be with you."(p158). Not only does Gil-Martin incite Robert to murderous acts against others, but eventually even against his own life, certain that his divine fate is unchangeable, "for he has me fully convinced that no act of mine can mar the eternal counsel, or in the smallest degree alter or extenuate one event which was decreed before the foundations of the world were laid." (p164). Ironically, in his post-script remarks recounting the discovery of Robert's grave 100 years later, the unnamed editor (the book was originally published anonymously, and Hogg himself appears as one of the characters) suggests a different fate for Robert, since by the act of suicide he had "committed that act for which, according to the tenets he embraced, there was no remission, and which consigned his memory and his name to everlasting detestation."(p175).
-GODLY GADFLY (April 2002)
NB: for my analysis of this book, see my review (dated April 26, 2002) of ISBN#1590170253.
Completely Misrepresents Predestination & Runs Many a Rabbit Trail!.......2005-10-10
I tried to like this novel because as one who believes in predestination, I thought it would show some of the opposing arguments in fictional form; it failed to do this. James Hogg merely shows us a deranged human being (nothing new there!) who murders because he feels that he is 'destined for heaven' no matter what he does. Yes, he might have been saved from the fires of hell, but it would have been by God's grace, not by his own good or evil works. Isn't this what the New Testament is all about-grace in spite of man's evil doing? Whether one is predestined or 'chooses good or evil' makes no difference in the end-what matters is who saves you from your own mortal destiny which is death. This story fails to show any unique theological and/or psychological perspective. I was dissatisfied with the author's far-fetched and anti-logical presentation of a doctrine he clearly did not understand.
None better.......2004-08-05
The depth of this novel is amazing. Visit Edinburgh on a misty night and you will see it is not set in the past.
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The Private Memoirs and Confessions of a Justified Sinner
James Hogg
Manufacturer: IndyPublish.com
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ASIN: 1404326022 |
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