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Thesis Defense
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