Cyclic branched coverings of knots and quandle homology

Details Cyclic branched coverings of knots and quandle homology Cyclic branched coverings of knots and quandle homology

2010-12-16

arxiv.org/abs/1012.3729v3

Mathematics

Geometric Topology

28 pages. Version 3: subsections 5.3 and 7.1 are slightly modified, accepted for publication in the Pacific Journal of Mathema

Scientific paper

We give a construction of quandle cocycles from group cocycles, especially, for any integer p \geq 3, quandle cocycles of the dihedral quandle R_p from group cocycles of the cyclic group Z/p. We will show that a group 3-cocycle of Z/p gives rise to a non-trivial quandle 3-cocycle of R_p. When p is an odd prime, since dim_{F_p} H_Q^3(R_p; F_p) = 1, our 3-cocycle is a constant multiple of the Mochizuki 3-cocycle up to coboundary. Dually, we construct a group cycle represented by a cyclic branched covering branched along a knot K from the quandle cycle associated with a colored diagram of K.

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