Fundamental classes of negatively curved manifolds cannot be represented by products of manifolds

2008/04/21 by Clara Loeh, Loeh, Clara · 1 citation
Computer Science · Mathematics · #32Q05 #57N65 #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0804.3242

openalex publication_date 2008/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On homology classes not representable by products

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