Bounded cohomology and homotopy colimits
arXiv:2103.15614
Abstract
The comparison map from bounded cohomology to singular cohomology plays an important role in the study of bounded cohomology theory and its applications. The vanishing and covering theorems of Gromov and Ivanov show interesting and useful properties of the comparison map under appropriate assumptions. We discuss an approach to these theorems, based on the general homotopy-theoretic properties of the comparison map, and obtain new proofs and refined versions of these results.
23 pages; there are changes in the terminology; more examples and applications are added; the exposition is improved