##### Department of Mathematics,

University of California San Diego

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### Math 292

## Sihao Ma

#### University of Notre Dame

## The Borel and genuine $C_2$-equivariant Adams spectral sequences

##### Abstract:

The Segal conjecture suggests that the 2-completed $C_2$-equivariant sphere is equivalent to its homotopy completion. However, the genuine $C_2$-equivariant Adams spectral sequence for the $C_2$-equivariant sphere is not isomorphic to the Borel one. In this talk, I will show that the Borel $C_2$-equivariant Adams spectral sequence can be obtained from the genuine one through a degree shifting of the negative cone with connecting differentials shortened. I will also show that the Borel $C_2$-equivariant Adams spectral sequence is related to some classical Adams spectral sequences, whose $E_2$-terms are computable through the Curtis algorithm.

Host: Zhouli Xu

### March 14, 2023

### 4:30 PM

APM 7218

Research Areas

Geometry and Topology****************************