On measure homology of mildly wild spaces

2025/06/03 by Thilo Kuessner, Kuessner, Thilo, Janusz Przewocki +3
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2506.03368

Abstract

We prove injectivity of the canonical map from singular homology to measure homology for certain ``mildly wild" spaces, that is, certain spaces not having the homotopy type of a CW-complex, but having countable fundamental groups.

Citations

• Topological realisations of absolute Galois groups
• Proportionality Principle for the Lipschitz simplicial volume
• Archipelago groups
• Piecewise straightening and Lipschitz simplicial volume
• Simplicial volume of compact manifolds with amenable boundary
• (Bounded) continuous cohomology and Gromov proportionality principle
• Covering maps for locally path-connected spaces
• Measure homology and singular homology are isometrically isomorphic

Related

• Measure homology and singular homology are isometrically isomorphic
• The homology core and invariant measures
• A note on measure homology
• Semi-coarse Spaces, Homotopy and Homology
• Universal finite functorial semi-norms