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.


  • 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.

Show description

Read Online or Download Theta Functions and Knots PDF

Similar calculus books

Radiation in Enclosures: Elliptic Boundary Value Problem (Scientific Computation)

Over the past part century, the improvement and checking out of prediction versions of combustion chamber functionality were an ongoing activity on the overseas Flame learn origin (IFRF) in IJmuiden within the Netherlands and at many different learn corporations. This activity has introduced forth a hierarchy of roughly typical numerical types for warmth move predictions, specifically for the prediction of radiative warmth move.

Advanced Basic Meta-analysis: Version 1.10

In accordance with the becoming emphasis on precision within the summarization and integration of analysis literature, complex uncomplicated Meta-Analysis offers an summary of ideas, options, and systems utilized in meta-analysis. The ebook and software program supply an built-in and accomplished mixture of meta-analytic instruments for the statistical integration of autonomous examine effects.

Numerical Solution of Partial Differential Equations—III, SYNSPADE 1975: Proceedings of the Third Symposium on the Numerical Solution of Partial Differential ... College Park, Maryland, May 19-24, 1975

Numerical answer of Partial Differential Equations—III: Synspade 1975 presents details pertinent to these tough difficulties in partial differential equations displaying a few form of singular habit. This booklet covers a number of themes, together with the mathematical versions and their relation to test in addition to the habit of options of the partial differential equations concerned.

Understanding Analysis (Undergraduate Texts in Mathematics)

Newly formatted for Kindle, this energetic introductory textual content exposes the scholar to the rewards of a rigorous learn of features of a true variable. In every one bankruptcy, casual discussions of questions that provide research its inherent fascination are through particular, yet now not overly formal, advancements of the recommendations had to make experience of  them.

Extra resources for Theta Functions and Knots

Sample text

Download PDF sample

Rated 4.30 of 5 – based on 41 votes