Thin Circle Valued Morse Functions For Knots In S3
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Thin Circle Valued Morse Functions For Knots In S3
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Author : Fabiola Manjarrez-Gutierrez
language : en
Publisher:
Release Date : 2008
Thin Circle Valued Morse Functions For Knots In S3 written by Fabiola Manjarrez-Gutierrez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
An Invitation To Morse Theory
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Author : Liviu Nicolaescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-02
An Invitation To Morse Theory written by Liviu Nicolaescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-02 with Mathematics categories.
This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
4 Manifolds And Kirby Calculus
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Author : Robert E. Gompf
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
4 Manifolds And Kirby Calculus written by Robert E. Gompf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Presents an exposition of Kirby calculus, or handle body theory on 4-manifolds. This book includes such topics as branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces.
Introduction To Vassiliev Knot Invariants
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Author : S. Chmutov
language : en
Publisher: Cambridge University Press
Release Date : 2012-05-24
Introduction To Vassiliev Knot Invariants written by S. Chmutov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-24 with Mathematics categories.
A detailed exposition of the theory with an emphasis on its combinatorial aspects.
Grid Homology For Knots And Links
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Author : Peter S. Ozsváth
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-11-30
Grid Homology For Knots And Links written by Peter S. Ozsváth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-30 with Education categories.
Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams.
Bordered Heegaard Floer Homology
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Author : Robert Lipshitz
language : en
Publisher:
Release Date : 2018
Bordered Heegaard Floer Homology written by Robert Lipshitz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Floer homology categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 1998
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Computational Topology
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Author : Herbert Edelsbrunner
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-31
Computational Topology written by Herbert Edelsbrunner and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-31 with Mathematics categories.
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Foliations And The Geometry Of 3 Manifolds
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Author : Danny Calegari
language : en
Publisher: Clarendon Press
Release Date : 2007-05-17
Foliations And The Geometry Of 3 Manifolds written by Danny Calegari and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-17 with Mathematics categories.
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Lectures On Field Theory And Topology
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-23
Lectures On Field Theory And Topology written by Daniel S. Freed and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-23 with Mathematics categories.
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.