A casson-lin type invariant for links

Eric Harper, Nikolai Saveliev

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In 1992, Xiao-Song Lin constructed an invariant h(K) of knots K ⊂ S3 via a signed count of conjugacy classes of irreducible SU(2) representations of π 1(S3 - K) with trace-free meridians. Lin showed that h(K) equals one half times the knot signature of K. Using methods similar to Lin's, we construct an invariant h(L) of two-component links L ⊂ S3. Our invariant is a signed count of conjugacy classes of projective SU(2) representations of π 1 (S3 - L) with a fixed 2-cocycle and corresponding nontrivial w2. We show that h(L) is, up to a sign, the linking number of L.

Original languageEnglish (US)
Pages (from-to)139-154
Number of pages16
JournalPacific Journal of Mathematics
Volume248
Issue number1
DOIs
StatePublished - 2010
Externally publishedYes

Keywords

  • Braid
  • Link group
  • Projective representation

ASJC Scopus subject areas

  • Mathematics(all)

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