Kan subdivision and products of simplicial sets
Vegard Fjellbo, John Rognes
TL;DR
This paper investigates the relationship between Kan subdivision and products of simplicial sets, showing that the canonical map's geometric realization has contractible point inverses, simplifying understanding of their interaction.
Contribution
It proves that the canonical map from the Kan subdivision of a product to the product of Kan subdivisions is simple, with contractible point inverses upon geometric realization.
Findings
The canonical map is simple.
Geometric realization has contractible point inverses.
Provides insight into Kan subdivision behavior.
Abstract
The canonical map from the Kan subdivision of a product of finite simplicial sets to the product of the Kan subdivisions is a simple map, in the sense that its geometric realization has contractible point inverses.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models