Volume 12, issue 1 (2012)

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

Thilo Kuessner

Algebraic & Geometric Topology 12 (2012) 155–213
Abstract

For a closed locally symmetric space M = ΓGK and a representation ρ: G GL(N, ) we consider the pushforward of the fundamental class in H(BGL(¯)) and a related invariant in K(¯) . We discuss the nontriviality of this invariant and we generalize the construction to cusped locally symmetric spaces of –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/