Speaker:  Carlos Segovia González (Universidad Nacional Autónoma de México)

Topic:  Extension of free actions over surfaces

Abstract:  Oriented, nonoriented and unitary bordism have certain module structures. We are interested in the unitary case which is a free module over the integers with even degrees. In the case of equivariant unitary bordism for a compact Lie group, it has been shown that for certain cases, we have a structure of free module (with respect to the usual unitary bordism) with generators in even degrees. Just to mention, Landweber proved the case of cyclic groups, Stong-Ossa the abelian groups, Löffer-Comezaña for compact abelian Lie groups and there are some proofs for metacyclic groups. The general case is known as the unitary evenness conjecture (UEC). This conjecture will imply that in equivariant bordism there is no torsion. A particular case will be that all free action of a finite group over a compact oriented surface “always” extends to a non-necessarily free action over a 3-manifold. In this talk we will see a counterexample that this is not always the case, which gives a counterexample of (UEC). A complete obstruction is given by the quotient of the 2-homology H_2(G) by the toral classes, known as the Bogomolov multiplier. The first counterexample published is a group of order 3^5.

Date: Nov 12, 2022 

Time: 16:00

Meet:  meet.google.com/qro-urbs-sdf
 

Listing: https://researchseminars.org/seminar/7tepemathseminars