A01=Razvan Gelca
Author_Razvan Gelca
Category=PBKD
Category=PBP
Chern-Simons Theory
ChernAcAEURA"Simons Theory
Chern–Simons Theory
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Knots
Linking Number
Skein Modules
Theta Functions
Topological Quantum Field Theory
Product details
- ISBN 9789814520577
- Publication Date: 24 Jul 2014
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
