An Extension Of Cassons Invariant To Rational Homology Spheres

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An Extension of Casson's Invariant. (AM-126), Volume 126

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Author : Kevin Walker
Publisher : Princeton University Press
ISBN 13 : 140088246X
Total Pages : 150 pages
Book Rating : 4.4/5 (8 download)

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.

An Extension of Casson's Invariant to Rational Homology Spheres

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Author : Kevin Michael Walker
Publisher :
ISBN 13 :
Total Pages : 66 pages
Book Rating : 4.:/5 (7 download)

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:

An Extension of Casson's Invariant

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Author : Kevin Walker
Publisher :
ISBN 13 : 9780691087665
Total Pages : 131 pages
Book Rating : 4.0/5 (876 download)

Book Synopsis An Extension of Casson's Invariant by : Kevin Walker

Download or read book An Extension of Casson's Invariant written by Kevin Walker and published by . This book was released on 1992 with total page 131 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.

Invariants of Homology 3-Spheres

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Author : Nikolai Saveliev
Publisher : Springer Science & Business Media
ISBN 13 : 3662047055
Total Pages : 229 pages
Book Rating : 4.6/5 (62 download)

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.

An Extension of Casson's Invariant

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Author : Kevin Walker
Publisher : Princeton University Press
ISBN 13 : 9780691025322
Total Pages : 148 pages
Book Rating : 4.0/5 (253 download)

Book Synopsis An Extension of Casson's Invariant by : Kevin Walker

Download or read book An Extension of Casson's Invariant written by Kevin Walker and published by Princeton University Press. This book was released on 1992-03-23 with total page 148 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.

Chern-Simons Gauge Theory: 20 Years After

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Author : Jørgen E. Andersen
Publisher : American Mathematical Soc.
ISBN 13 : 0821853538
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Chern-Simons Gauge Theory: 20 Years After by : Jørgen E. Andersen

Download or read book Chern-Simons Gauge Theory: 20 Years After written by Jørgen E. Andersen and published by American Mathematical Soc.. This book was released on 2011 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.

Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140

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Author : Christine Lescop
Publisher : Princeton University Press
ISBN 13 : 1400865158
Total Pages : 156 pages
Book Rating : 4.4/5 (8 download)

Book Synopsis Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 by : Christine Lescop

Download or read book Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 written by Christine Lescop and published by Princeton University Press. This book was released on 2014-09-08 with total page 156 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.

Geometry and Physics

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Author : H. Pedersen
Publisher : CRC Press
ISBN 13 : 1000110850
Total Pages : 766 pages
Book Rating : 4.0/5 (1 download)

Book Synopsis Geometry and Physics by : H. Pedersen

Download or read book Geometry and Physics written by H. Pedersen and published by CRC Press. This book was released on 2021-01-07 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."

A Survey of Knot Theory

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Author : Akio Kawauchi
Publisher : Birkhäuser
ISBN 13 : 3034892276
Total Pages : 431 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis A Survey of Knot Theory by : Akio Kawauchi

Download or read book A Survey of Knot Theory written by Akio Kawauchi and published by Birkhäuser. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

Seiberg Witten Gauge Theory

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Author : Matilde Marcolli
Publisher : Springer
ISBN 13 : 9386279002
Total Pages : 224 pages
Book Rating : 4.3/5 (862 download)

Book Synopsis Seiberg Witten Gauge Theory by : Matilde Marcolli

Download or read book Seiberg Witten Gauge Theory written by Matilde Marcolli and published by Springer. This book was released on 1999-12-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

European Congress of Mathematics

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Author : Antal Balog
Publisher : Springer Science & Business Media
ISBN 13 : 9783764354978
Total Pages : 364 pages
Book Rating : 4.3/5 (549 download)

Book Synopsis European Congress of Mathematics by : Antal Balog

Download or read book European Congress of Mathematics written by Antal Balog and published by Springer Science & Business Media. This book was released on 1998-07-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua

The Generalized Casson Invariant for Two-fold Branched Covers of the Three-sphere and the Jones Polynomial

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Author : David T. Mullins
Publisher :
ISBN 13 :
Total Pages : 130 pages
Book Rating : 4.F/5 ( download)

Book Synopsis The Generalized Casson Invariant for Two-fold Branched Covers of the Three-sphere and the Jones Polynomial by : David T. Mullins

Download or read book The Generalized Casson Invariant for Two-fold Branched Covers of the Three-sphere and the Jones Polynomial written by David T. Mullins and published by . This book was released on 1990 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Intelligence Of Low Dimensional Topology 2006

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Author : J Scott Carter
Publisher : World Scientific
ISBN 13 : 9814475734
Total Pages : 398 pages
Book Rating : 4.8/5 (144 download)

Book Synopsis Intelligence Of Low Dimensional Topology 2006 by : J Scott Carter

Download or read book Intelligence Of Low Dimensional Topology 2006 written by J Scott Carter and published by World Scientific. This book was released on 2007-05-29 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the contributions from the international conference “Intelligence of Low Dimensional Topology 2006,” which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.

Lectures on the Topology of 3-Manifolds

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Author : Nikolai Saveliev
Publisher : Walter de Gruyter
ISBN 13 : 3110250365
Total Pages : 220 pages
Book Rating : 4.1/5 (12 download)

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 2011-12-23 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in low-dimensional topology has been very quick in the last three decades, leading to the solutions of many difficult problems. Among the earlier highlights of this period was Casson's λ-invariant that was instrumental in proving the vanishing of the Rohlin invariant of homotopy 3-spheres. The proof of the three-dimensional Poincaré conjecture has rendered this application moot but hardly made Casson's contribution less relevant: in fact, a lot of modern day topology, including a multitude of Floer homology theories, can be traced back to his λ-invariant. The principal goal of this book, now in its second revised edition, remains providing an introduction to the low-dimensional topology and Casson's theory; it also reaches out, when appropriate, to more recent research topics. The book covers some classical material, such as Heegaard splittings, Dehn surgery, and invariants of knots and links. It then proceeds through the Kirby calculus and Rohlin's theorem to Casson's invariant and its applications, and concludes with a brief overview of recent developments. The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic and differential topology, including the fundamental group, basic homology theory, transversality, and Poincaré duality on manifolds.

Quantum Topology - Proceedings Of The Conference

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Author : David N Yetter
Publisher : World Scientific
ISBN 13 : 9814551597
Total Pages : 390 pages
Book Rating : 4.8/5 (145 download)

Book Synopsis Quantum Topology - Proceedings Of The Conference by : David N Yetter

Download or read book Quantum Topology - Proceedings Of The Conference written by David N Yetter and published by World Scientific. This book was released on 1994-08-19 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the conference on quantum topology, held at Kansas State University, Manhattan, KS, 24 - 28 March 1993.Quantum topology is a rapidly growing field of mathematics dealing with the recently discovered interactions between low-dimensional topology, the theory of quantum groups, category theory, C∗-algebra theory, gauge theory, conformal and topological field theory and statistical mechanics. The conference, attended by over 60 mathematicians and theoretical physicists from Canada, Denmark, England, France, Japan, Poland and the United States, was highlighted by lecture series given by Louis Kauffman, Univ. of Illinois at Chicago and Nicholai Reshetikhin, Univ. of Califonia, Berkeley.

Five Decades As A Mathematician And Educator: On The 80th Birthday Of Professor Yung-chow Wong

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Author : Kwong-yu Chan
Publisher : World Scientific
ISBN 13 : 9814500100
Total Pages : 599 pages
Book Rating : 4.8/5 (145 download)

Book Synopsis Five Decades As A Mathematician And Educator: On The 80th Birthday Of Professor Yung-chow Wong by : Kwong-yu Chan

Download or read book Five Decades As A Mathematician And Educator: On The 80th Birthday Of Professor Yung-chow Wong written by Kwong-yu Chan and published by World Scientific. This book was released on 1995-07-01 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:My Early Life, 1913–1948 (Y-C Wong)On the Eigenvalues and Numerical Range of a Quaternionic Matrix (Y-H Au-Yeung)Monopoles as Fibre Bundles and Strings as Infinite Rank Tensors (H-M Chan & S T Tsou)Approximation by Affine Functions (J-T Chan)A Review on Optimal Design for Mixture Models (L-Y Chan)Griffiths' Formalism on the Calculus of Variations via Exterior Differential Systems (W-S Cheung)Change of Measures, Likelihood Ratio Martingales and Some Applications (T L Lai)Beyond the Impossibility of a 16-Square Identity (K Y Lam & P Yiu)Lie Group Homomorphisms which Induce Isomorphisms of Representation Rings (S P Lam)A Lifting Theorem, and Rings with Isomorphic Matrix Rings (T Y Lam)On Ternary Equations in Square-Free and Prime Variables (Y-L Lau, M-C Leung & M-C Liu)Instantons and Three-Manifolds (R Lee)Some Results on the c-Numerical Range (C-K Li & Y-T Poon)A Matrix Formulation of the Complex Flag Manifolds (Q-K Lu)The Integral Formulas of the Pontrjagin Characteristic Forms on an Oriented Differentiable Manifold (X-M Mei)On the Construction of Tensor Fields and Connections on the Frame Bundle (K P Mok)Cellular Manufacturing Systems: Formulation and Algorithmic Issues (S M Ng)Which Inscribed N-Gon in an Ellipse has the Longest Perimeter? (M K Siu & K M Tsang)Hyperbolicity Problems in Function Theory (Y-T Siu)Extreme Positive Operators on Convex Cones (B-S Tam)The Golden Mean and Its Way into Physics (B Y Tong) Readership: Students and scientists in mathematics. keywords:

Bulletin of the American Mathematical Society

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Author :
Publisher :
ISBN 13 :
Total Pages : 736 pages
Book Rating : 4.4/5 (91 download)

Book Synopsis Bulletin of the American Mathematical Society by :

Download or read book Bulletin of the American Mathematical Society written by and published by . This book was released on 1994 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: