Ranicki-Weiss assembly and the Steenrod construction
Anibal M. Medina-Mardones
TL;DR
This paper demonstrates that the Ranicki-Weiss assembly functor can be factored through the Steenrod cup-i coalgebra, revealing a deeper connection between chain complex presheaves and Steenrod algebra structures.
Contribution
It establishes a full and faithful factorization of the assembly functor through the Steenrod cup-i coalgebra, linking algebraic topology and homological algebra.
Findings
Full faithfulness of the factorization
Connection between assembly functor and Steenrod coalgebra
Enhanced understanding of chain complex presheaves
Abstract
We show that the Ranicki-Weiss assembly functor, going from chain complex valued presheaves on a simplicial complex to comodules over its Alexander-Whitney coalgebra, factors fully faithfully through the category of comodules over its Steenrod cup- coalgebra.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Algebraic structures and combinatorial models