University of Arkansas Topology Seminar: 11/12/2020

Speaker: Trevor Nakamura

Title: Cohomology of the symmetric group with twisted coefficients

For any group G and an abelian group A, the second cohomology of G with coefficients in A is in one-to-one correspondence with group extensions of G by A. In 2018 Brendle and Margalit showed there is a non-split extension of the symmetric group by the level 4 braid group. In this talk I will begin by discussing the connection between subgroups of the braid group and extensions of the symmetric group. Then I will construct the 2–cocylce corresponding to the extension of the symmetric group by abelianization of the pure braid group and show this is an element of order 2.



BACK TO SCHEDULE