Graph homology of moduli space of pointed real curves of genus zero

Details Graph homology of moduli space of pointed real curves of genus zero Graph homology of moduli space of pointed real curves of genus zero

2007-02-07

arxiv.org/abs/math/0702165v2

Mathematics

Algebraic Topology

38 pages, 4 figures. To appear in Selecta Mathematica

Scientific paper

The moduli space $\bar{M}_S^\sigma(R)$ parameterizes the isomorphism classes of $S$-pointed stable real curves of genus zero which are invariant under relabeling by the involution $\sigma$. This moduli space is stratified according to the degeneration types of $\sigma$-invariant curves. The degeneration types of $\sigma$-invariant curves are encoded by their dual trees with additional decorations. We construct a combinatorial graph complex generated by the fundamental classes of strata of $\bar{M}_S^\sigma(R)$. We show that the homology of $\bar{M}_S^\sigma(R)$ is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of $\bar{M}_S^\sigma(R)$.

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