The Dupont Homotopy Formula and Stellar Subdivision
Benjamin I. Albert
TL;DR
This paper investigates whether the classical Dupont homotopy construction in algebraic topology remains compatible with stellar subdivision, a key operation in triangulated manifolds, within the context of effective field theories.
Contribution
It examines the compatibility of Dupont's homotopy with stellar subdivision, linking algebraic topology to effective field theory applications.
Findings
Dupont homotopy is compatible with stellar subdivision under certain conditions.
Compatibility results inform the use of homotopy in renormalization group analysis.
The study bridges classical topology and modern field theory techniques.
Abstract
The Dupont homotopy, a classical construction in the algebraic topology of triangulated smooth manifolds, has been revived in the last decade in the construction of an effective field theory where it appears as a propagator. In this paper, we ask a question of relevance to the renormalization group of this theory: is Dupont's construction compatible with stellar subdivision?
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models