Some perspective on Homotopy obstructions
Satya Mandal, Bibekananda Mishra

TL;DR
This paper explores the structure of homotopy obstruction sets associated with projective modules over a noetherian ring, establishing isomorphisms under certain conditions and connecting these sets to Chow groups.
Contribution
It provides new insights into the structure of homotopy obstruction sets and their invariance under certain conditions, linking them to Chow groups.
Findings
Homotopy obstruction sets are isomorphic for projective modules with the same rank and determinant.
Established a natural map from homotopy obstruction sets to Chow groups.
Extended understanding of the structure and invariance of homotopy obstructions.
Abstract
Throughout will denote commutative noetherian ring, with , and denote a projective -module with . In \cite{MM1} we considered the Homotopy obstruction sets , which has a structure of an abelian monoid, under suitable regularity and other conditions. In this article, we provide some perspective on these sets . Under similar regularity and other conditions, we prove if are two projective -modules, with and , then . Further, for any projective -module with , we define a natural set theoretic map , where Chow groups of codimension cycles.
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Taxonomy
TopicsRings, Modules, and Algebras · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
