By Răzvan Gelca

This booklet provides the connection among classical theta capabilities and knots. it truly is in line with a unique thought of Răzvan Gelca and Alejandro Uribe, which converts Weil's illustration of the Heisenberg workforce on theta features to a knot theoretical framework, by means of giving a topological interpretation to a definite brought about illustration. It additionally explains how the discrete Fourier rework will be regarding three- and four-dimensional topology.

Theta capabilities and Knots should be learn in views. Readers with an curiosity in theta features or knot conception can find out how the 2 are similar. these attracted to Chern–Simons idea will locate the following an advent utilizing the best case, that of abelian Chern–Simons conception. additionally, the development of abelian Chern–Simons thought is predicated solely on quantum mechanics and never on quantum box concept because it is generally done.

Both the idea of theta features and coffee dimensional topology are awarded intimately, so one can underline how deep the relationship among those basic mathematical matters is. as a result the publication is self-contained with a unified presentation. it's appropriate for a complicated graduate path, in addition to for self-study.

Contents:

  • Prologue
  • A Quantum Mechanical Prototype
  • Surfaces and Curves
  • The Theta services 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 crew Perspective
  • An Epilogue — Abelian Chern–Simons Theory

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

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