Locally symmetric spaces and K–theory of number fields

Kuessner, Thilo

doi:10.2140/agt.2012.12.155

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Locally symmetric spaces and $K$–theory of number fields

Thilo Kuessner

Algebraic & Geometric Topology 12 (2012) 155–213

DOI: 10.2140/agt.2012.12.155

Abstract

For a closed locally symmetric space $M = Γ ∖ G ∕ K$ and a representation $ρ : G \to GL (N, ℂ)$ we consider the pushforward of the fundamental class in $H_{*} (BGL (\bar{ℚ}))$ and a related invariant in $K_{*} (\bar{ℚ}) \otimes ℚ$ . We discuss the nontriviality of this invariant and we generalize the construction to cusped locally symmetric spaces of $ℝ$ –rank one.

Keywords

symmetric spaces, algebraic $K$–theory, volume, Borel class

Mathematical Subject Classification 2000

Primary: 57R19, 53C35, 57M50

Secondary: 11R70, 22E46

References

Publication

Received: 15 November 2010

Revised: 18 November 2011

Accepted: 18 November 2011

Published: 24 February 2012

Authors

Thilo Kuessner
Korea Institute for Advanced Study, School of Mathematics Hoegi-ro 85 Dongdaemun-Gu Seoul 130-722 South Korea
http://wwwmath.uni-muenster.de/u/kuessner/

Volume 12, issue 1 (2012)