An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants PDF full book. Access full book title An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants by Paul Feehan. Download full books in PDF and EPUB format.
Author: Paul Feehan
Publisher: American Mathematical Soc.
ISBN: 147041421X
Category : Mathematics
Languages : en
Pages : 254
Get Book Here
Book Description
The authors prove an analogue of the Kotschick–Morgan Conjecture in the context of monopoles, obtaining a formula relating the Donaldson and Seiberg–Witten invariants of smooth four-manifolds using the -monopole cobordism. The main technical difficulty in the -monopole program relating the Seiberg–Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible monopoles, namely the moduli spaces of Seiberg–Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of monopoles. In this monograph, the authors prove—modulo a gluing theorem which is an extension of their earlier work—that these intersection pairings can be expressed in terms of topological data and Seiberg–Witten invariants of the four-manifold. Their proofs that the -monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Mariño, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with and odd appear in earlier works.
Author: Paul Feehan
Publisher: American Mathematical Soc.
ISBN: 147041421X
Category : Mathematics
Languages : en
Pages : 254
Get Book Here
Book Description
The authors prove an analogue of the Kotschick–Morgan Conjecture in the context of monopoles, obtaining a formula relating the Donaldson and Seiberg–Witten invariants of smooth four-manifolds using the -monopole cobordism. The main technical difficulty in the -monopole program relating the Seiberg–Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible monopoles, namely the moduli spaces of Seiberg–Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of monopoles. In this monograph, the authors prove—modulo a gluing theorem which is an extension of their earlier work—that these intersection pairings can be expressed in terms of topological data and Seiberg–Witten invariants of the four-manifold. Their proofs that the -monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Mariño, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with and odd appear in earlier works.
Author: Robert Friedman
Publisher: Springer Science & Business Media
ISBN: 3662030284
Category : Mathematics
Languages : en
Pages : 532
Get Book Here
Book Description
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.
Author: Robert Friedman, John W. Morgan
Publisher: American Mathematical Soc.
ISBN: 9780821886861
Category : Four-manifolds (Topology).
Languages : en
Pages : 236
Get Book Here
Book Description
This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.
Author: Jan de Gier
Publisher: Springer Nature
ISBN: 3030624978
Category : Mathematics
Languages : en
Pages : 798
Get Book Here
Book Description
MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.
Author: Garth Baker
Publisher: Birkhäuser
ISBN: 3034888953
Category : Mathematics
Languages : en
Pages : 166
Get Book Here
Book Description
This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.
Author: János Kollár
Publisher: American Mathematical Soc.
ISBN: 082180894X
Category : Geometry, Algebraic
Languages : en
Pages : 469
Get Book Here
Book Description
Author: Akio Kawauchi
Publisher: Springer Science & Business Media
ISBN: 9783764351243
Category : Mathematics
Languages : en
Pages : 454
Get Book Here
Book Description
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 knot theory from its very beginnings to today's most recent research results. The topics include Alexander polynomials, Jones type polynomials, and Vassiliev invariants. With its appendix containing many useful tables and an extended list of references with over 3,500 entries it is an indispensable book for everyone concerned with knot theory. The book can serve as an introduction to the field for advanced undergraduate and graduate students. Also researchers working in outside areas such as theoretical physics or molecular biology will benefit from this thorough study which is complemented by many exercises and examples.
Author: Stefan Behrens
Publisher: Oxford University Press
ISBN: 0192578383
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
Book Description
Based on Fields medal winning work of Michael Freedman, this book explores the disc embedding theorem for 4-dimensional manifolds. This theorem underpins virtually all our understanding of topological 4-manifolds. Most famously, this includes the 4-dimensional Poincaré conjecture in the topological category. The Disc Embedding Theorem contains the first thorough and approachable exposition of Freedman's proof of the disc embedding theorem, with many new details. A self-contained account of decomposition space theory, a beautiful but outmoded branch of topology that produces non-differentiable homeomorphisms between manifolds, is provided, as well as a stand-alone interlude that explains the disc embedding theorem's key role in all known homeomorphism classifications of 4-manifolds via surgery theory and the s-cobordism theorem. Additionally, the ramifications of the disc embedding theorem within the study of topological 4-manifolds, for example Frank Quinn's development of fundamental tools like transversality are broadly described. The book is written for mathematicians, within the subfield of topology, specifically interested in the study of 4-dimensional spaces, and includes numerous professionally rendered figures.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 684
Get Book Here
Book Description
Author: Steven Bell
Publisher: Springer Science & Business Media
ISBN: 9783540629955
Category : Mathematics
Languages : en
Pages : 324
Get Book Here
Book Description
The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.
