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A K-theoretic Selberg trace formula

MPS-Authors
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Mesland,  Bram
Max Planck Institute for Mathematics, Max Planck Society;

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Şengün,  Mehmet Haluk
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

arXiv:1904.04728.pdf
(Preprint), 255KB

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Citation

Mesland, B., Şengün, M. H., & Wang, H. (2020). A K-theoretic Selberg trace formula. In R. E.. Curto, W. Helton, & H. Lin (Eds.), Operator theory, operator algebras and their interactions with geometry and topology: Ronald G. Douglas memorial volume (pp. 403-424). Cham: Birkhäuser.


Cite as: http://hdl.handle.net/21.11116/0000-0007-AD87-E
Abstract
Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L^2(G/H) associated to test functions. In this paper we present a cohomological interpretation of the trace formula involving the K-theory of the maximal group C*-algebras of G and H. As an application, we exploit the role of group C*-algebras as recipients of higher indices of elliptic differential operators and we obtain the index theoretic version of the Selberg trace formula developed by Barbasch and Moscovici from ours.