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Invariants Of Homology 3 Spheres
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Book Synopsis Invariants of Homology 3-Spheres by : Nikolai Saveliev
Download or read book Invariants of Homology 3-Spheres written by Nikolai Saveliev and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematic exposition of the diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered include: constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, and Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. The text will be a valuable source for both the graduate student and researcher in mathematics and theoretical physics.
Book Synopsis Casson's Invariant for Oriented Homology Three-Spheres by : Selman Akbulut
Download or read book Casson's Invariant for Oriented Homology Three-Spheres written by Selman Akbulut and published by Princeton University Press. This book was released on 2014-07-14 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the spring of 1985, A. Casson announced an interesting invariant of homology 3-spheres via constructions on representation spaces. This invariant generalizes the Rohlin invariant and gives surprising corollaries in low-dimensional topology. In the fall of that same year, Selman Akbulut and John McCarthy held a seminar on this invariant. These notes grew out of that seminar. The authors have tried to remain close to Casson's original outline and proceed by giving needed details, including an exposition of Newstead's results. They have often chosen classical concrete approaches over general methods. For example, they did not attempt to give gauge theory explanations for the results of Newstead; instead they followed his original techniques. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Casson's Invariant for Oriented Homology 3-spheres by : Selman Akbulut
Download or read book Casson's Invariant for Oriented Homology 3-spheres written by Selman Akbulut and published by . This book was released on 1985 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Casson's Invariant for Oriented Homology 3-spheres by : Selman Akbulut
Download or read book Casson's Invariant for Oriented Homology 3-spheres written by Selman Akbulut and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Topology of 3-manifolds by : Nikolai Saveliev
Download or read book Lectures on the Topology of 3-manifolds written by Nikolai Saveliev and published by Walter de Gruyter. This book was released on 1999 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Surgery Formula for the Casson-Walker Invariant by : Christine Lescop
Download or read book Global Surgery Formula for the Casson-Walker Invariant written by Christine Lescop and published by Princeton University Press. This book was released on 1996-01-11 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.
Book Synopsis Casson's Invariant for Oriented Homology 3-spheres by : James A. Bernhard
Download or read book Casson's Invariant for Oriented Homology 3-spheres written by James A. Bernhard and published by . This book was released on 1993 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Perturbative Invariants of Rational Homology 3-spheres Can be Recovered from the LMO Invariant by : Takahito Kuriya
Download or read book The Perturbative Invariants of Rational Homology 3-spheres Can be Recovered from the LMO Invariant written by Takahito Kuriya and published by . This book was released on 2010 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Invariants by : Tomotada Ohtsuki
Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."
Book Synopsis An Extension of Casson's Invariant. (AM-126), Volume 126 by : Kevin Walker
Download or read book An Extension of Casson's Invariant. (AM-126), Volume 126 written by Kevin Walker and published by Princeton University Press. This book was released on 2016-03-02 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities. A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.
Book Synopsis Solitons, Geometry, and Topology: On the Crossroad by : V. M. Buchstaber
Download or read book Solitons, Geometry, and Topology: On the Crossroad written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 1997 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Heegaard Floer Homology of Certain 3-manifolds and Cobordism Invariants by : Daniel Selahi Durusoy
Download or read book Heegaard Floer Homology of Certain 3-manifolds and Cobordism Invariants written by Daniel Selahi Durusoy and published by . This book was released on 2008 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Unified Quantum SO(3) and SU(2) Invariants for Rational Homology 3-spheres by : Irmgard Adelheid Bühler
Download or read book Unified Quantum SO(3) and SU(2) Invariants for Rational Homology 3-spheres written by Irmgard Adelheid Bühler and published by . This book was released on 2010 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces by : S. K. Donaldson
Download or read book Geometry of Low-Dimensional Manifolds: Volume 1, Gauge Theory and Algebraic Surfaces written by S. K. Donaldson and published by Cambridge University Press. This book was released on 1990 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distinguished researchers reveal the way different subjects (topology, differential and algebraic geometry and mathematical physics) interact in a text based on LMS Durham Symposium Lectures.
Book Synopsis An Extension of Casson's Invariant to Rational Homology Spheres by : Kevin Michael Walker
Download or read book An Extension of Casson's Invariant to Rational Homology Spheres written by Kevin Michael Walker and published by . This book was released on 1989 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Invariants by : Tomotada Ohtsuki
Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.
Book Synopsis On Casson's Invariant of Oriented Homology Three-spheres by : Chung-Hsing OuYang
Download or read book On Casson's Invariant of Oriented Homology Three-spheres written by Chung-Hsing OuYang and published by . This book was released on 1988 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
