##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Robert Burklund

#### MIT

## Classification of manifolds and the Adams spectral sequence

##### Abstract:

A classical question in differential topology is the following: Classify all simply-connected, closed, smooth (2n)-manifolds whose only non-trivial homology groups are $H_0, H_n$ and $H_{2n}$. In this talk I will survey the history of the high dimensional side of this question and how its resolution requires a surprisingly deep understanding of the Adams spectral sequence computing the stable homotopy groups of spheres. Time permitting, I will then discuss how the situation changes as we relax our topological restrictions on the manifold (for example allowing $H_{n-e}$, $H_{n-e+1}$, ... $H_{n+e}$ to be non-trivial for a small number e). \\ \\ This talk represents joint work with Jeremy Hahn and Andy Senger.

Host: Zhouli Xu

### February 9, 2021

### 10:30 AM

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

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