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Trudy Mat. Inst. Steklova, 2004, Volume 247, Pages 59–73 (Mi tm10)  

Lipschitz Cohomology, Novikov Conjecture, and Expanders

A. N. Dranishnikov

University of Florida

Abstract: We present sufficient conditions for the cohomology of a closed aspherical manifold to be proper Lipschitz in the sense of Connes–Gromov–Moscovici. 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 by Carlsson and Pedersen. 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 examples of exotic groups.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 247, 50–63

Bibliographic databases:
UDC: 515.165
Received in April 2004

Citation: A. N. Dranishnikov, “Lipschitz Cohomology, Novikov Conjecture, and Expanders”, Geometric topology and set theory, Collected papers. Dedicated to the 100th birthday of professor Lyudmila Vsevolodovna Keldysh, Trudy Mat. Inst. Steklova, 247, Nauka, MAIK Nauka/Inteperiodika, M., 2004, 59–73; Proc. Steklov Inst. Math., 247 (2004), 50–63

Citation in format AMSBIB
\Bibitem{Dra04}
\by A.~N.~Dranishnikov
\paper Lipschitz Cohomology, Novikov Conjecture, and Expanders
\inbook Geometric topology and set theory
\bookinfo Collected papers. Dedicated to the 100th birthday of professor Lyudmila Vsevolodovna Keldysh
\serial Trudy Mat. Inst. Steklova
\yr 2004
\vol 247
\pages 59--73
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm10}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2168163}
\zmath{https://zbmath.org/?q=an:1107.57016}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 247
\pages 50--63


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