Unitary embeddings and local Gorenstein duality for classifying spaces
Unitary embeddings and local Gorenstein duality for classifying spaces
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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.听 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.