Condensed and solid maths in the study of cohomological finiteness conditions

Condensed and solid maths in the study of cohomological finiteness conditions

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Peter Kropholler, University of Southampton

Online Talk 

Zoom link: https://princeton.zoom.us/j/92116764865

Passcode: 114700

We’ll look at how the Clausen–Scholze theory of condensed and solid abelian groups can be brought to bear on the study of cohomological finiteness conditions for topological groups. This is very much ‘work in progress’ building on discussions with Lukas Brantner, Rudradip Biswas, and Robert K. One of the main benefits of this approach is that one can work with abelian categories that have enough projectives and so there are algebraic Farrell–Tate cohomology theories available. We’ll study how these can be applied and compare with the practical results of Corob Cook and Castellano that applies to Castellano–Weigel cohomology.