Wikibooks

Topological String Theory Methods of Computer-aided Drug Design/Printable version

< Topological String Theory Methods of Computer-aided Drug Design
This is the print version of Topological String Theory Methods of Computer-aided Drug Design
You won't see this message or any elements not part of the book's content when you print or preview this page.


Topological String Theory Methods of Computer-aided Drug Design

The current, editable version of this book is available in Wikibooks, the open-content textbooks collection, at
https://en.wikibooks.org/wiki/Topological_String_Theory_Methods_of_Computer-aided_Drug_Design

Permission is granted to copy, distribute, and/or modify this document under the terms of the Creative Commons Attribution-ShareAlike 3.0 License.

Knots, HOMFLY-PT Polynomial, Chern-Simons Theory and Surgery

This chapter covers knot theory and its invariants, including, especially, HOMFLY-PT polynomials. We explain Witten's viewpoint: these polynomials can be interpreted as the vacuum expectation value of Wilson loop operators in Chern-Simons Theory with gauge group   and the fundamental representation. This easily leads to the generalization of HOMFLY-PT polynomials to arbitrary gauge groups and representations. We then introduce Guadagnini's amalgamation of Chern-Simons theory and Dehn surgery: this allows the computation of HOMFLY-PT polynomials in an arbitrary  -manifold   with given surgery presentation. This includes all  -manifolds, due to a result by Lickorish and Wallace.

Contents edit

  1. Knot theory
  2. Link invariants
  3. HOMFLY-PT polynomials
  4. Chern-Simons Theory
  5. Surgery
  6. HOMFLY-PT polynomials in arbitrary  -manifolds


Retrieved from "https://en.wikibooks.org/w/index.php?title=Topological_String_Theory_Methods_of_Computer-aided_Drug_Design/Printable_version&oldid=4008861"