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FUNDAMENTAL CLASSES OF NEGATIVELY CURVED MANIFOLDS CANNOT BE REPRESENTED BY PRODUCTS OF MANIFOLDS

By Clara Löh

Abstract

Not every singular homology class is the push-forward of the fundamental class of some manifold. In the same spirit, one can study the following problem: Which singular homology classes are the push-forward of the fundamental class of a given type of manifolds? In the present article, we show that the fundamental classes of negatively curved manifolds cannot be represented by a non-trivial product of manifolds. This observation sheds some light on the functorial semi-norm on singular homology given by products of compact surfaces

Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.313.1779
Provided by: CiteSeerX
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