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arXiv · 1204.4999

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

Urtzi Buijs·Aniceto Murillo
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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.

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Urtzi Buijs, Aniceto Murillo. 2013-02-01. Algebraic models of non-connected spaces and homotopy theory of $L_\infty$ algebras. https://arxiv.org/abs/1204.4999

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