Morava K-theory of infinite groups and Euler characteristic

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• Irakli Patchkoria (University of Aberdeen)
• Friday 16 June 2023, 10:00-11:00
• Seminar Room 1, Newton Institute.

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HHHW06 - HHH follow on: Homotopy: fruit of the fertile furrow

Abstract: Given an infinite discrete group G with a finite model for the classifying space for proper actions, one can define the Euler characteristic of G and the orbifold Euler characteristic of G. In this talk we will discuss higher chromatic analogues of these invariants in the sense of stable homotopy theory. We will study the Morava K-theory of G and associated Euler characteristic, and give a character formula for the Lubin-Tate theory of G. This will generalise the results of Hopkins-Kuhn-Ravenel from finite to infinite groups and the K-theoretic results of Adem, Lück and Oliver from chromatic level one to higher chromatic levels. At the end we will mention explicit computations for some arithmetic groups and also discuss connections with special values of zeta functions. This talk is mostly based on a joint work with Lück and Schwede.

This talk is part of the Isaac Newton Institute Seminar Series series.

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