Theta Functions and Knots

Nonfiction, Science & Nature, Mathematics, Topology
Cover of the book Theta Functions and Knots by Răzvan Gelca, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Răzvan Gelca ISBN: 9789814520591
Publisher: World Scientific Publishing Company Publication: May 21, 2014
Imprint: WSPC Language: English
Author: Răzvan Gelca
ISBN: 9789814520591
Publisher: World Scientific Publishing Company
Publication: May 21, 2014
Imprint: WSPC
Language: English

This book presents the relationship between classical theta functions and knots. It is based on a novel idea of Răzvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology.

Theta Functions and Knots can be read in two perspectives. Readers with an interest in theta functions or knot theory can learn how the two are related. Those interested in Chern–Simons theory will find here an introduction using the simplest case, that of abelian Chern–Simons theory. Moreover, the construction of abelian Chern–Simons theory is based entirely on quantum mechanics and not on quantum field theory as it is usually done.

Both the theory of theta functions and low dimensional topology are presented in detail, in order to underline how deep the connection between these two fundamental mathematical subjects is. Hence the book is self-contained with a unified presentation. It is suitable for an advanced graduate course, as well as for self-study.

Contents:

  • Prologue
  • A Quantum Mechanical Prototype
  • Surfaces and Curves
  • The Theta Functions Associated to a Riemann Surface
  • From Theta Functions to Knots
  • Some Results About 3- and 4-Dimensional Manifolds
  • The Discrete Fourier Transform and Topological Quantum Field Theory
  • Theta Functions in the Quantum Group Perspective
  • An Epilogue — Abelian Chern–Simons Theory

Readership: Graduate students and young researchers with an interest in complex analysis, mathematical physics, algebra geometry and low dimensional topology.
Key Features:

  • A detailed study of the skein modules of the linking number, which provide the simplest example of a skein module (skein modules have become a major object of study in combinatorial topology)
  • A complete discussion of the facts from low dimensional topology (Kirby's theorem, the Lickorish–Walace theorem, Wall's non-additivity of the signature) which are fundamental in Chern–Simons theory
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book presents the relationship between classical theta functions and knots. It is based on a novel idea of Răzvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology.

Theta Functions and Knots can be read in two perspectives. Readers with an interest in theta functions or knot theory can learn how the two are related. Those interested in Chern–Simons theory will find here an introduction using the simplest case, that of abelian Chern–Simons theory. Moreover, the construction of abelian Chern–Simons theory is based entirely on quantum mechanics and not on quantum field theory as it is usually done.

Both the theory of theta functions and low dimensional topology are presented in detail, in order to underline how deep the connection between these two fundamental mathematical subjects is. Hence the book is self-contained with a unified presentation. It is suitable for an advanced graduate course, as well as for self-study.

Contents:

Readership: Graduate students and young researchers with an interest in complex analysis, mathematical physics, algebra geometry and low dimensional topology.
Key Features:

More books from World Scientific Publishing Company

Cover of the book Physics on Ultracold Quantum Gases by Răzvan Gelca
Cover of the book Regulation of Foreign Investment by Răzvan Gelca
Cover of the book Understanding and Preventing Sudden Death by Răzvan Gelca
Cover of the book Energy Studies by Răzvan Gelca
Cover of the book Uncertainty Modeling in Knowledge Engineering and Decision Making by Răzvan Gelca
Cover of the book Lectures on Quantum Mechanics by Răzvan Gelca
Cover of the book Wavefronts and Rays as Characteristics and Asymptotics by Răzvan Gelca
Cover of the book Modeling Developing Countries' Policies in General Equilibrium by Răzvan Gelca
Cover of the book Interfuel Substitution by Răzvan Gelca
Cover of the book Myanmar by Răzvan Gelca
Cover of the book Sir Francis Ronalds by Răzvan Gelca
Cover of the book From East to West by Răzvan Gelca
Cover of the book Top the TOEFL by Răzvan Gelca
Cover of the book Simulations of Tropical Cyclone in Regional Climate Models by Răzvan Gelca
Cover of the book Waves and Rays in Seismology by Răzvan Gelca
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy