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Theta Functions And Knots

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Title: Theta Functions And Knots
Description: 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.
Authors: Razvan Gelca
Resource Type: eBook.
Subjects: Functions, Theta, Knot theory
Categories: MATHEMATICS / Topology, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Complex Analysis
Database: eBook Collection (EBSCOhost)
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  – Type: ebook-pdf
  – Type: ebook-epub
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 810364
RelevancyScore: 1057
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1057.36352539063
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  Data: Theta Functions And Knots
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  Label: Description
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  Data: 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.
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  Data: <searchLink fieldCode="AR" term="%22Razvan+Gelca%22">Razvan Gelca</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Functions%2C+Theta%22">Functions, Theta</searchLink><br /><searchLink fieldCode="DE" term="%22Knot+theory%22">Knot theory</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 514.2242
        Scheme: ddc
        Type: prePub
      – Code: 515.984
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Functions, Theta
        Type: general
      – SubjectFull: Knot theory
        Type: general
    Titles:
      – TitleFull: Theta Functions And Knots
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Razvan Gelca
      – PersonEntity:
          Name:
            NameFull: Razvan Gelca
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2014
            – D: 23
              M: 07
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9789814520577
            – Type: isbn-electronic
              Value: 9789814520584
            – Type: isbn-electronic
              Value: 9789814520591
          Titles:
            – TitleFull: Theta Functions And Knots
              Type: main
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