2002/05/15 by Alexander Dranishnikov, A. Dranishnikov, Dranishnikov, A.
Mathematics · #05C10 #20F65 #53C23 #57R22 #57S30 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:05C10 #msc:20F65 #msc:53C23 #msc:57R22 #msc:57S30
paper · pdf · doi:10.48550/arxiv.math/0205172
19 pages
openalex publication_date 2002/05/15 · arxiv created 2003/07/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present sufficient conditions for the cohomology of a closed aspherical manifold to be proper Lipschitz in sense of Connes-Gromov-Moscovici [CGM]. The conditions are stated in terms of the Stone-Čech compactification of the universal cover of a manifold. We show that these conditions are formally weaker than the sufficient conditions for the Novikov conjecture given in [CP]. Also we show that the Cayley graph of the fundamental group of a closed aspherical manifold with proper Lipschitz cohomology cannot contain an expander in the coarse sense. In particular, this rules out a Lipschitz cohomology approach to the Novikov Conjecture for recent Gromov's examples of exotic groups.