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

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

2012-04-23

arxiv.org/abs/1204.4999v1

Mathematics

Algebraic Topology

Scientific paper

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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