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Theta Functions And Knots by Razvan Gelca (Texas Tech Univ, Usa) at Abbey's Bookshop,
Theta Functions And Knots
— —
Razvan Gelca (Texas Tech Univ, Usa)

Theta Functions And Knots

Razvan Gelca (Texas Tech Univ, Usa)

$302.99

Hardback

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English
World Scientific Publishing Co Pte Ltd
22 May 2014
Complex analysis, complex variables; Topology
This book presents the relationship between classical theta functions and knots. It is based on a novel idea of Razvan 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.
By:  
Imprint:   World Scientific Publishing Co Pte Ltd
Country of Publication:   Singapore
Dimensions:   Height: 229mm,  Width: 155mm,  Spine: 30mm
Weight:   794g
ISBN:   9789814520577
ISBN 10:   9814520578
Pages:   468
Publication Date:  
Audience:   College/higher education ,  Further / Higher Education
Format:   Hardback
Publisher's Status:   Active
Some Historical Facts; 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 and Quantum Groups; An Epilogue - Abelian Chern - Simons Theory.

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