Higher homotopy operations and cohomology
David Blanc, Mark W. Johnson, James M. Turner
TL;DR
This paper explores the relationship between higher homotopy operations and cohomological obstructions, showing how topologically defined operations can be identified with Dwyer-Kan-Smith obstructions under certain conditions.
Contribution
It establishes a connection between higher homotopy operations and cohomological obstructions, providing a new perspective on rectifying homotopy-commutative diagrams.
Findings
Higher homotopy operations can be identified with cohomological obstructions.
The identification holds under mild assumptions.
Provides a unified view of homotopy operations and cohomology.
Abstract
We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics