Amenable covers and relative bounded cohomology

2024/07/01 by Pietro Capovilla, Capovilla, Pietro
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2407.01140

Abstract

We establish a relative version of Gromov's Vanishing Theorem in the presence of amenable open covers with small multiplicity, extending a result of Li, Löh, and Moraschini. Our approach relies on Gromov's theory of multicomplexes.

Related

• Bounded cohomology of amenable covers via classifying spaces
• Gromov's theory of multicomplexes with applications to bounded cohomology and simplicial volume
• Amenable covers and l¹-invisibility
• Bounded cohomology and homotopy colimits
• Pairings, duality, amenability and bounded cohomology