Rice University

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Seminar

Mathematics

Speaker: Daniel Studenmund
University of Utah

Topology Seminar: Cohomology of the lamplighter group

Monday, February 20, 2017
4:00 PM  to 5:00 PM

427  Herman Brown Hall
Rice University
6100 Main St
Houston, Texas, USA

A duality group has a pairing exhibiting isomorphisms between its homology and cohomology groups. Examples include solvable Baumslag-Solitar groups and arithmetic groups over number fields by work of Borel and Serre. Many naturally occurring groups fail to be duality groups, but are morally very close. In this talk we make this precise with the notion of a semiduality group, and prove that the lamplighter group is a semiduality group. This illustrates methods used to prove the rank 1 case of a general conjecture that certain arithmetic groups in positive characteristic are semiduality groups, building on the result of Borel-Serre. This talk covers work joint with Kevin Wortman.

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