Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Bikei homology

Pages: 23 – 35

DOI: http://dx.doi.org/10.4310/HHA.2017.v19.n1.a2

Authors

Sam Nelson (Department of Mathematical Sciences, Claremont McKenna College, Claremont, California, U.S.A.)

Jake Rosenfield (Department of Mathematical Sciences, Claremont McKenna College, Claremont, California, U.S.A.)

Abstract

We introduce a modified homology and cohomology theory for involutory biquandles (also known as bikei ). We use bikei $2$-cocycles to enhance the bikei counting invariant for unoriented knots and links as well as unoriented and non-orientable knotted surfaces in $\mathbb{R}^4$.

Keywords

bikei, involutory biquandle, cocycle invariant, bikei homology

2010 Mathematics Subject Classification

57M25, 57M27

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Published 8 March 2017