Series of Academic Activities of School and Institute of Mathematics in 2020（the 198th）：

Associate Professor Seung Yeop Yang  Kyungpook National University

Report title: Annihilation of Rack and Quandle Homology Groups of Finite Quasigroup Quandles

Reporter: Associate Professor Seung Yeop Yang Kyungpook National University

Reporting time: September 9, 2020 13:00-14:00 PM

Report location: Zoom ID: 882 5486 0575; PW: 6VtwZq

School contact: Wang Xiao wangxiaotop@jlu.edu.cn

Report summary：

It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. The first general results in this direction were obtained independently about 2001 by R. A. Litherland and S. Nelson, and P. Etingof and M. Grana. The result of Litherland-Nelson is generalized by Niebrzydowski and Przytycki and in particular, they prove that the torsion part of the homology of the dihedral quandle of order 3 is annihilated by 3. In Niebrzydowski-Przytycki's paper, it is conjectured that for a finite quasigroup quandle, torsion of its homology is annihilated by the order of the quandle. The conjecture is proved by T. Nosaka for finite Alexander quasigroup quandles. In this talk, we prove the conjecture in full generality, and find upper bounds for the torsion of rack homology of some finite quandles.

Brief introduction of the speaker:

Associate Professor Seung Yeop Yang, currently working at Kyungpook National University in South Korea. He is mainly engaged in the research of low-dimensional topology and knot theory.