Algebraic models of non-connected spaces and homotopy theory of L∞ algebras
Abstract
We develop a homotopy theory of L∞ 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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