Some results about the Kauffman bracket skein module of the twist knot exterior

Rǎzvan Gelca, Fumikazu Nagasato

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we list in explicit form the factoring relations of the Kauffman bracket skein module (KBSM for short) of a twist knot exterior. This is done using curves decorated by characters of irreducible SL(2, C)-representations. In the process, we exhibit a relation which holds in the KBSM of the knot exterior, called the minimal relation. In the final section we prove that, when specializing the variable of the Kauffman bracket at t = -1, the minimal relation becomes the defining polynomial of the SL(2, C)-character variety of the twist knot.

Original languageEnglish
Pages (from-to)1095-1106
Number of pages12
JournalJournal of Knot Theory and its Ramifications
Volume15
Issue number8
DOIs
StatePublished - Oct 2006

Keywords

  • A-polynomial
  • Character varieties
  • Colored Kauffman brackets
  • Kauffman bracket skein module
  • Tunnel number

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