Mathematics Colloquium
Date: Wednesday, 17 April 2024
Time: 2:00 - 3:30 PM
Venue: Seminar Hall
Stiefel-Whitney Classes of Representations
Steven Spallone
IISER Pune.
17-04-24

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Abstract

An orthogonal representation of a finite group has invariants living in the (mod 2) group cohomology, called Stiefel–Whitney Classes (SWCs). The first two SWCs vanish iff the representation lifts to the spin group. If a vector bundle arises from balancing a G-bundle with a represention of G, then its SWCs can be deduced from the SWC of the representation. This talk surveys my research group's work in computing SWCs for familiar groups, as well as the spinoriality problem.