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In search for homology of Bol-Moufang quasigroups

Jozef Przytycki ⟨przytyck@gmail.com⟩

Abstract:

0ur goal is to initiate (co)homology theory for quasigroups of Bol-Moufang. Our approach which has its roots in the work of Eilenberg and his coauthors (MacLane, Cartan) is to analyze extensions of a quasigroup (X,X) by an affine quasigroup (A,A) of the same type. We study these extensions not to classify them but to have the first glimpse at their homology via their second and third boundary operation, 2(x,y) and 3(x,y,z) respectively. We compute the second homology groups for all distinguishing examples of Bol-Moufang quasigroups described by Phillips and Vojtechovsky. We specualte about use of homology of Bol-Moufang quasigroups in Knot Theory. It is a joint work with Anthony Christiana, Ben Clingenpeel, Huizheng Guo, Jinseok Oh, and Anna Zamojska-Dzienio.

Status: Accepted

Collection: Low-Dimensional Topology

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