Obstruction sequences to homotopy equivalences

2025/09/22 by Coline Emprin, Emprin, Coline · 1 citation
Decision Sciences · Mathematics · #Algebraic structures and combinatorial models #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #math.QA

paper · pdf · doi:10.48550/arxiv.2509.17895

openalex publication_date 2025/09/22 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We develop an obstruction theory for the existence of gauge equivalences in complete differential graded Lie algebras. Specifically, this theory provides a characterization of homotopy equivalences between differential graded algebras governed by operads or properads, potentially colored in a groupoid. We apply this framework to establish new homotopy equivalence results in both algebraic topology and algebraic geometry, with a particular focus on the study of minimal models for highly connected varieties.

Citations

• Integration theory of Lie-graph algebras
• Simplicial properadic homotopy
• Properadic coformality of spheres
• Kaledin classes and formality criteria
• Homotopical operadic calculus in positive characteristic
• Curved operadic calculus
• Pre-Calabi-Yau algebras and topological quantum field theories
• Properadic homotopical calculus
• Massey products for graph homology
• On fibrations with formal elliptic fibers
• Homotopy Batalin-Vilkovisky algebras

Cited by

• Some examples of DG-Lie formality transfer

Related

• Models for Operads
• Algebraic operads up to homotopy
• Obstruction theory for algebras over an operad
• Rational obstruction theory and rational homotopy sets
• Gauge equivalence for complete L_∞-algebras