Algebraic models of non-connected spaces and homotopy theory of\n L_\∞ algebras

2012/04/23 by Urtzi Buijs, Buijs, Urtzi, Aniceto Murillo +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1204.4999

openalex publication_date 2012/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a homotopy theory of L_\∞ algebras based on the\nLawrence-Sullivan construction, a complete differential graded Lie algebra\nwhich, as we show, satisfies the necessary properties to become the right\ncylinder in this category. As a result, we obtain a general procedure to\nalgebraically model the rational homotopy type of non-connected spaces.\n

Citations

• Deformations of algebras over operads and Deligne's conjecture

Cited by

• Higher Lie and Leibniz algebras

Related

• The Milnor-Moore theorem for L_\∞ algebras in rational homotopy\n theory
• L_infty rational homotopy of mapping spaces
• Homotopy operations and rational homotopy type
• Enriched Differential Lie Algebras in Topology
• Disconnected rational homotopy theory