##### Department of Mathematics,

University of California San Diego

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### Math 292 - Topology Seminar

## Yang Hu

#### University of Oregon

## Metastable complex vector bundles over complex projective spaces

##### Abstract:

We study unstable topological complex vector bundles over complex projective spaces. It is a classical problem in algebraic topology to count the number of rank $r$ bundles over $\mathbb{C}P^n$ (with $1 < r < n$) having fixed Chern class data. A particular case is when the Chern data is trivial, which we call the vanishing Chern enumeration. We apply a modern tool, Weiss calculus, to produce the vanishing Chern enumeration in the first two unstable cases (which belong to what we call the "metastable" range, following Mark Mahowald), namely rank $(n - 1)$ bundles over $\mathbb{C}P^n$ for $n > 2$, and rank $(n - 2)$ bundles over $\mathbb{C}P^n$ for $n > 3$.

Host: Zhouli Xu

### April 26, 2022

### 1:00 PM

https://ucsd.zoom.us/j/99777474063

Password: topology

Research Areas

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