Algebraic models of non-connected spaces and homotopy theory of $L_{\infty }$ algebras

Abstract

We develop a homotopy theory of $L_{\infty }$ algebras based on the Lawrence-Sullivan construction, a complete differential graded Lie algebra which, as we show, satisfies the necessary properties to become the right cylinder in this category. As a result, we obtain a general procedure to algebraically model the rational homotopy type of non-connected spaces.

Final version, to appear in Advances in Mathematics. 44 pages

Cited by in corpus (1)

• Higher Lie and Leibniz algebras