Bounded cohomology and negatively curved manifolds

Sungwoon Kim; Inkang Kim

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arXiv · 1111.6412

Bounded cohomology and negatively curved manifolds

Sungwoon Kim·Inkang Kim

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Abstract

We study the bounded fundamental class in the top dimensional bounded cohomology of negatively curved manifolds with infinite volume. We prove that the bounded fundamental class of $M$ vanishes if $M$ is geometrically finite. Furthermore, when $M$ is a $\mathbb{R}$-rank one locally symmetric space, we show that the bounded fundamental class of $M$ vanishes if and only if the Riemannian volume form on $M$ is the differential of a bounded differential form on $M$.

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BibTeX RIS

Sungwoon Kim, Inkang Kim. 2011-11-28. Bounded cohomology and negatively curved manifolds. https://arxiv.org/abs/1111.6412

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