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In this paper we show that the homology of a certain natural compactificationof the moduli space, introduced by Kontsevich in his study of Witten'sconjectures, can be described completely algebraically as the homology of acertain differential graded Lie algebra. This two-parameter family isconstructed by using a Lie cobracket on the space of noncommutative 0-forms, astructure which corresponds to pinching simple closed curves on a Riemannsurface, to deform the noncommutative symplectic geometry described byKontsevich in his subsequent papers.

Noncommutative geometry and compactifications of the moduli space of curves