论文信息 - L2-Cohomology and group cohomology

L2-Cohomology and group cohomology

LETY be an arbitrary topological space and let I be a countable group which acts on Y. In this paper we study some homotopy theoretic invariants of such actions. In many respects, our treatment parallels more standard discussions of Betti numbers and the Euler characteristic. The main novelty is that our invariants are defined using the concept of I-dimension (Von Neumann dimension) of singular L,-cohomology. If r is a finite group which acts on a finite dimensional vector space V, the I-dimension of V is given by 1 dim, I’ = ___ ord (r) dim V. (0.1)

Jeff Cheeger | J. Cheeger | M. Gromov | Mikhael Gromov

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