Locally symmetric spaces and K–theory of number fields

Kuessner, Thilo¹

¹Korea Institute for Advanced Study, School of Mathematics Hoegi-ro 85, Dongdaemun-Gu, Seoul 130-722, South Korea

Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 155-213

Résumé

For a closed locally symmetric space M = Γ∖G∕K and a representation ρ: G → GL(N, ℂ) we consider the pushforward of the fundamental class in H∗(BGL(ℚ¯)) and a related invariant in K∗(ℚ¯) ⊗ ℚ. We discuss the nontriviality of this invariant and we generalize the construction to cusped locally symmetric spaces of ℝ–rank one.

Détail

DOI : 10.2140/agt.2012.12.155

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

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