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****************************
