Bounded differential forms and coinvariants of bounded functions

2023/11/13 by Francesco Milizia, Milizia, Francesco · 1 citation
Mathematics · #57N65 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2311.07731

openalex publication_date 2023/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a group G acting cocompactly on a smooth manifold M by deck transformations, there is an integration map, defined recently by Kato, Kishimoto and Tsutaya, from the top-degree bounded de Rham cohomology of M to the coinvariants ℓ^∞(G)_G. We generalize its definition and show that it is an isomorphism. In the presence of boundary, a relative version of bounded de Rham cohomology is considered.

Cited by

• Geometric effects of hyperbolic cohomology classes on Kähler manifolds (with an appendix by Benoît Claudon)

Related

• Cohomology of coinvariant differential forms
• Integrated differential geometry. Commutative and noncommutative
• Bounded Cohomology Classes of Exact Forms
• Equivariant Differential Cohomology
• The Essence of de Rham Cohomology