##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Calista Bernard

#### Stanford University

## Twisted homology operations

##### Abstract:

In the 70s, Fred Cohen and Peter May gave a description of the mod $p$ homology of a free $E_n$-algebra in terms of certain homology operations, known as Dyer--Lashof operations, and the Browder bracket. These operations capture the failure of the $E_n$ multiplication to be strictly commutative, and they prove useful for computations. After reviewing the main ideas from May and Cohen's work, I will discuss a framework to generalize these operations to homology with certain twisted coefficient systems and give a complete classification of twisted operations for $E_{\infty}$-algebras. I will also explain computational results that show the existence of new operations for $E_2$-algebras.

Host: Zhouli Xu

### December 1, 2020

### 10:30 AM

### Zoom information: Meeting ID: 933 6734 4286 Password: topology

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