A triangulation of a homotopy-Deligne-Mumford compactification of the Moduli of curves

Mathematics – Geometric Topology

Scientific paper

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10 pages

Scientific paper

We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the compactification we construct to the Deligne-Mumford compactification so that the inverse image of each point is contractible. In particular our compactification is homotopy equivalent to the Deligne-Mumford compactification.

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