This e-book offers the connection among classical theta services and knots. it's in keeping with a unique notion of Razvan Gelca and Alejandro Uribe, which converts Weil's illustration of the Heisenberg team on theta services to a knot theoretical framework, by means of giving a topological interpretation to a definite caused illustration. It additionally explains how the discrete Fourier remodel will be relating to three- and four-dimensional topology.

Theta features and Knots should be learn in views. Readers with an curiosity in theta capabilities or knot thought can learn the way the 2 are similar. these attracted to Chern–Simons concept will locate the following an creation utilizing the easiest case, that of abelian Chern–Simons thought. additionally, the development of abelian Chern–Simons concept is predicated totally on quantum mechanics and never on quantum box concept because it is generally performed. .

either the speculation of theta capabilities and occasional dimensional topology are offered intimately, which will underline how deep the relationship among those basic mathematical topics is. as a result the e-book is self-contained with a unified presentation. it's appropriate for a sophisticated graduate direction, in addition to for self-study. .

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

Show description

Read or Download Theta Functions and Knots PDF

Similar Algebraic Geometry books

An Introduction to Algebraic Geometry and Algebraic Groups (Oxford Graduate Texts in Mathematics)

An obtainable textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the speculation of affine algebraic teams from first ideas. construction at the heritage fabric from algebraic geometry and algebraic teams, the textual content presents an advent to extra complicated and specialized fabric.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The speculation of elliptic curves is special by way of its lengthy background and by means of the range of the equipment which were utilized in its research. This e-book treats the mathematics technique in its smooth formula, by using uncomplicated algebraic quantity conception and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal workforce of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and worldwide fields.

Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics)

This seriously class-tested booklet is an exposition of the theoretical foundations of hyperbolic manifolds. it's a either a textbook and a reference. A uncomplicated wisdom of algebra and topology on the first 12 months graduate point of an American college is thought. the 1st half is anxious with hyperbolic geometry and discrete teams.

Extra info for Theta Functions and Knots

Show sample text content

Rated 4.84 of 5 – based on 15 votes