Monday December 4th, 2023 | |
Time: | 10:30 AM - 12:00 PM |
Title: | Invariants of Real Vector Bundles |
Speaker: | Jiahao Hu, Stony Brook University |
Location: | Math P-131 |
Abstract: | |
For a compact smooth manifold with corners (or finite CW-complex) X, we can prescribe a finite set of spin or $spin^h$ manifolds (possibly with boundary) mapping into it so that every real vector bundle over X is determined, up to stable equivalence, by the Dirac indices of the real vector bundle when pulled-back onto those prescribed spin or $spin^h$ manifolds. Our proof features a thorough study of indices of Dirac operators on $spin^h$ manifolds and a general duality between cycles and cocycles. Dissertation Advisor: Dennis Sullivan |