Homotopy Algebras are Homotopy Algebras

1999/07/22 by Martin Markl, Markl, Martin · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT

paper · pdf · doi:10.48550/arxiv.math/9907138

LaTeX 2.09, 31 pages, article 12pt + bezier, substantially revised

openalex publication_date 1999/07/22 · arxiv created 2002/06/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that strongly homotopy algebras (such as A_∞, C_∞, sh Lie, B_∞, G_∞,...) are homotopically invariant in the category of chain complexes. An important consequence is a rigorous proof that `strongly homotopy structures transfer over chain homotopy equivalences.'

Cited by

• Open-closed homotopy algebra in mathematical physics

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