  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.
