Simplicial sets, Postnikov systems, and bounded cohomology
Nikolai V. Ivanov
TL;DR
This paper develops a new approach to bounded cohomology using simplicial sets and Postnikov systems, extending key results from topological spaces to Kan simplicial sets.
Contribution
It introduces an extension of bounded cohomology theory to Kan simplicial sets, broadening its applicability beyond traditional topological spaces.
Findings
Bounded cohomology results are extended to Kan simplicial sets.
The approach unifies simplicial set theory with bounded cohomology.
New methods for analyzing topological invariants are proposed.
Abstract
The paper is devoted to an approach to the bounded cohomology theory based on the theories of simplicial sets and Postnikov systems. In particular, the main results of the bounded cohomology theory of topological spaces are extended to arbitrary Kan (fibrant) simplicial sets.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Topological and Geometric Data Analysis