Download e-book for kindle: Theta Functions and Knots by Răzvan Gelca

By Răzvan Gelca

This publication offers the connection among classical theta services and knots. it truly is in keeping with a singular notion of Răzvan Gelca and Alejandro Uribe, which converts Weil's illustration of the Heisenberg team on theta services to a knot theoretical framework, via giving a topological interpretation to a definite precipitated illustration. It additionally explains how the discrete Fourier rework might be concerning three- and four-dimensional topology.

Theta capabilities and Knots will be learn in views. Readers with an curiosity in theta features or knot idea can learn the way the 2 are similar. these attracted to Chern–Simons concept will locate right here an creation utilizing the best case, that of abelian Chern–Simons conception. in addition, the development of abelian Chern–Simons idea is predicated totally on quantum mechanics and never on quantum box concept because it is mostly done.

Both the speculation of theta features and coffee dimensional topology are offered intimately, with a view to underline how deep the relationship among those basic mathematical matters is. therefore the booklet is self-contained with a unified presentation. it truly is compatible for a complicated graduate direction, in addition to for self-study.

Contents:

  • Prologue
  • A Quantum Mechanical Prototype
  • Surfaces and Curves
  • The Theta capabilities linked to a Riemann Surface
  • From Theta services to Knots
  • Some effects approximately three- and four-dimensional Manifolds
  • The Discrete Fourier rework and Topological Quantum box Theory
  • Theta services within the Quantum team Perspective
  • An Epilogue — Abelian Chern–Simons Theory

Readership: Graduate scholars and younger researchers with an curiosity in advanced research, mathematical physics, algebra geometry and coffee dimensional topology.

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Theta Functions and Knots by Răzvan Gelca


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