Groups acting on buildings, operator K-theory, and Novikov's conjecture |
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Authors: | G G Kasparov and G Skandalis |
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Institution: | (1) Department of Mathematics, Institute of Chemical Physics, 142432 Chernogolovka, Moscow Region, USSR;(2) UFR de Mathématiques ERA 212, Université Paris 7, Tour 45-55, 5e étage, 2, pl. Jussieu, 75231 Paris cedex 05, France |
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Abstract: | The paper is devoted to the study of the KK-theory of Bruhat-Tits buildings. We develop a theory which is analogous to the corresponding theory for manifolds of nonpositive sectional curvature. We construct a C
*-algebra and a Dirac element associated to any simplicial complex. In the case of buildings, we construct, moreover, a dual Dirac element and compute its KK-products with the Dirac element. As a consequence, we prove the Novikov conjecture for discrete subgroups of linear adelic groups. In our study, we develop a KK-theoretic Poincaré duality for non-Hausdorff manifolds.Dedicated to Alexander Grothendieck on his sixtieth birthday |
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Keywords: | Operator K-theory Bruhat-Tits buildings Novikov's conjecture Poincaré duality |
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