Amenable covers and relative bounded cohomology
Pietro Capovilla
TL;DR
This paper extends Gromov's Vanishing Theorem to relative cases using amenable covers with small multiplicity, leveraging Gromov's multicomplex theory to broaden the theorem's applicability.
Contribution
It introduces a relative version of Gromov's Vanishing Theorem for amenable open covers, expanding previous results to new contexts.
Findings
Established a relative Vanishing Theorem for amenable covers
Extended previous results of Li, L"oh, and Moraschini
Utilized Gromov's multicomplexes in the proof
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, L\"oh, and Moraschini. Our approach relies on Gromov's theory of multicomplexes.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds