Bounded cohomology and negatively curved manifolds

2011/11/28 by Kim, Sungwoon, Kim, Inkang
#20F67 #53C23 #53C35 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1111.6412

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 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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