Twisted homology operations

Calista Bernard (Stanford University & University of Copenhagen)

Monday 22nd February 16:00-17:00 Online

Abstract

In the 70s, Fred Cohen and Peter May developed a theory of operations on the mod p homology En-algebras. These operations, usually referred to as Dyer--Lashof operations, capture the failure of the En multiplication to be strictly commutative, and they prove useful for computations. After giving a brief introduction to En-algebras and an overview of the key ideas from May and Cohen's work, I will discuss a framework to generalize these operations to homology with certain twisted coefficient systems and explain an application of these twisted operations to study homological stability. I will also give a complete classification of twisted operations for E-algebras and explain computational results on the homology of pure braid groups that show the existence of new operations for E2-algebras.

The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).


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