Quandle Cocycle Invariants

  • Scott Carter
  • Seiichi Kamada
  • Masahico Saito
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 142)

Abstract

Invariants in a state-sum form that are defined in a similar manner for both classical knots and knotted surfaces were first presented in [CJKLS03] (and announced in [CJKLS99]) using cocycles of quandle homology theory. The quandle cocycle knot invariants are natural generalizations of the Dijkgraaf-Witten invariant for 3-manifolds and other state-sum invariants. They have found important topological applications. In this chapter, we review these developments.

Keywords

Manifold Dition Agram Betti 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Scott Carter
    • 1
  • Seiichi Kamada
    • 2
  • Masahico Saito
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of South AlabamaMobileUSA
  2. 2.Department of MathematicsHiroshima UniversityHigashi-Hiroshima City, HiroshimaJapan
  3. 3.Department of MathematicsUniversity of South FloridaTampaUSA

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