Leray theorems for $l_1$-norms of infinite chains
Nikolai V. Ivanov
TL;DR
This paper extends Leray theorems to infinite chains in bounded cohomology, providing stronger results and generalizations of Gromov's theorems with elementary proofs.
Contribution
It introduces a broader version of Leray theorems for infinite chains and generalizes key results of Gromov's bounded cohomology theorems.
Findings
Stronger form of Gromov's Vanishing-finiteness theorem
Generalization of Gromov's Cutting-off theorem
Elementary proofs of the main results
Abstract
The paper is devoted to an adaptation of author's approach to Leray theorems in bounded cohomology theory to infinite chains. The main results are a stronger and more general form of Gromov's Vanishing-finiteness theorem and a generalization of the first part of his Cutting-of theorem. The proofs are elementary.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Historical and Scientific Studies