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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

Triple Point Homology Group Cohomology Theory Homology Theory Jones Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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