Algebraic & Geometric Topology

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

Thilo Kuessner

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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.

Article information

Algebr. Geom. Topol., Volume 12, Number 1 (2012), 155-213.

Received: 15 November 2010
Revised: 18 November 2011
Accepted: 18 November 2011
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R19: Algebraic topology on manifolds 53C35: Symmetric spaces [See also 32M15, 57T15] 57M50: Geometric structures on low-dimensional manifolds
Secondary: 11R70: $K$-theory of global fields [See also 19Fxx] 22E46: Semisimple Lie groups and their representations

symmetric spaces algebraic $K$–theory volume Borel class


Kuessner, Thilo. Locally symmetric spaces and $K$–theory of number fields. Algebr. Geom. Topol. 12 (2012), no. 1, 155--213. doi:10.2140/agt.2012.12.155.

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