Notes on the bounded cohomology theory

Abstract

The paper is devoted to a generalized and improved version of author's approach to Gromov bounded cohomology theory. In particular, the awkward countability assumption is removed and the aspects related to homological algebra are clarified. The exposition is largely self-contained.

95 pages. The statement of Covering theorem and proofs of this theorem and Vanishing theorem are corrected (Section 9). This does not affect the rest of the paper

Cited by in corpus (8)

• Leray theorems in bounded cohomology theory
• Amenability and Acyclicity in Bounded Cohomology Theory
• A remark on the Mayer-Vietoris double complex for singular cohomology
• Weakly bounded cohomology classes and a counterexample to a conjecture of Gromov
• Leray theorems for $l_1$-norms of infinite chains
• Bounded cohomology of amenable covers via classifying spaces
• Simplicial sets, Postnikov systems, and bounded cohomology
• Amenable covers and l^1-invisibility