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Theta functions and knots / Razvan Gelca.

By: Material type: TextTextPublication details: New Jersey : World Scientific, 2014.Description: xiv, 454 p. : illustrations ; 24 cmISBN:
  • 9789814520577 (hard cover : alk. paper)
Subject(s): DDC classification:
  • 515.984 23 G314
Contents:
1. Prologue-- 2. A quantum mechanical prototype-- 3. Surfaces and curves-- 4. The theta function associated to a Riemann surface-- 5. From theta functions to knots-- 6. Some results about 3 and 4 dimensional manifolds-- 7. The discrete Fourier transform and topological quantum field theory-- 8. Theta functions in the quantum group perspective-- 9. An epilogue- Abelian Chern-Simons theory-- Bibliography-- Index.
Summary: 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. People with an interest in theta functions or knot theory can learn how the two are related.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.984 G314 (Browse shelf(Opens below)) Available 136043
Total holds: 0

Includes bibliographical references and index.

1. Prologue--
2. A quantum mechanical prototype--
3. Surfaces and curves--
4. The theta function associated to a Riemann surface--
5. From theta functions to knots--
6. Some results about 3 and 4 dimensional manifolds--
7. The discrete Fourier transform and topological quantum field theory--
8. Theta functions in the quantum group perspective--
9. An epilogue- Abelian Chern-Simons theory--
Bibliography--
Index.

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. People with an interest in theta functions or knot theory can learn how the two are related.

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