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On the Berstein–Svarc theorem in dimension 2

Published online by Cambridge University Press:  01 March 2009

ALEXANDER N. DRANISHNIKOV  and
YULI B. RUDYAK
ALEXANDER N. DRANISHNIKOV
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL 32611, U.S.A. e-mail: dranish@math.ufl.edu; rudyak@math.ufl.edu
YULI B. RUDYAK
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL 32611, U.S.A. e-mail: dranish@math.ufl.edu; rudyak@math.ufl.edu
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Abstract

We prove that for any group π with cohomological dimension at least n the nth power of the Berstein class of π is nontrivial. This allows us to prove the following Berstein–Svarc theorem for all n:

Theorem. For a connected complex X with dim X = cat X = n, we have ≠ 0 whereis the Berstein class of X.

Previously it was known for n ≥ 3.

We also prove that, for every map f: M → N of degree ±1 of closed orientable manifolds, the fundamental group of N is free provided that the fundamental group of M is.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 407 - 413
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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