Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras

Antonini, Paolo; Buss, Alcides; Engel, Alexander; Siebenand, Timo

doi:10.1090/tran/8372

Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras
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by Paolo Antonini, Alcides Buss, Alexander Engel and Timo Siebenand PDF

Trans. Amer. Math. Soc. 374 (2021), 5071-5093 Request permission

Abstract:

We strengthen a result of Hanke–Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group C*-algebra holds for many other exotic group C*-algebras, in particular the one associated to the smallest strongly Morita compatible and exact crossed product functor used in the new version of the Baum–Connes conjecture. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

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