Yuichi Kabaya

Quandle homology and group homology

slide: PDF.
video: comming soon.
abstract:
A quandle is a set with a binary operation satisfying the axioms motivated by the properties of conjugation in a group. The (co)homology group of a quandle is defined using cubes' whose edges are labelled by elements of the quandle. On the other hand, the (co)homology of a group is defined using simplices' whose edges are labelled by elements of the group. In this talk, we first review quandles and quandle homology theory, then give some homomorphisms between quandle homology and group homology. In particular, we construct non-trivial cocycles of a quandle from cocycles of a group related to the quandle.