Unitary embeddings and local Gorenstein duality for classifying spaces

Natàlia Castellana, Universitat Autònoma de Barcelona

Online Talk 

Zoom link: https://princeton.zoom.us/j/96282936122

Passcode: 998749

The mod p cohomology of the classifying space of a compact Lie group G is a Noetherian algebra and it satisfies a duality property implied by a Gorenstein condition on its geometric cochains.  A proof of these two facts can be obtained from the existence of a faithful complex representation. Since the mod p cohomology of BG depends only on the p-local structure of G (determined by discrete p-toral subgroups and its conjugacy relations), one could ask whether other properties, like the ones mentioned, only depend on the p-local structure which is encoded in a category, the fusion systems. In this talk, I will explain results obtained in different collaborations (Cantarero, Morales, and Barthel, Heard, Valenzuela) which lead to a strategy and (partial) answers.