Free Lie Algebroids and the Space of Paths
نویسنده
چکیده
Among known algebro-geometric constructions that have the flavor of the space of unparametrized paths, one should mention the Kontsevich moduli stack M g,2(X, β) of stable maps from 2-pointed curves (C, x, y) of genus g into X, see [Ma]. Indeed, this stack consists of maps (C, x, y) → X for variable (C, x, y) modulo isomorphisms of curves, i.e., changes of parametrization. The points x and y serve as the beginning and end of a path. One of our main results, Theorem 7.3.5, constructs, in the case g = 0, a morphism from a certain formal neighborhood in M 0,2(X, β) into Π̂X . The case of n-pointed curves, n ≥ 3, can be treated similarly by considering the simplicial classifying space of Π̂X .
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