RELATIVE MEASURE HOMOLOGY AND CONTINUOUS BOUNDED COHOMOLOGY OF TOPOLOGICAL PAIRS

摘要

Measure homology was introduced by Thurston in his notes about the geometry and topology of 3-manifolds, where it was exploited in the computation of the simplicial volume of hyperbolic manifolds. Zastrow and Hansen independently proved that there exists a canonical isomorphism between measure homology and singular homology(on the category of CW-complexes), and it was then shown by L?h that, in the absolute case, such isomorphism is in fact an isometry with respect to the L1-seminorm on singular homology and the total variation seminorm on measure homology. Loh's result plays a fundamental role in the use of measure homology as a tool for computing the simplicial volume of Riemannian manifolds.