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

Abstract

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 ${\bar{M}}_S^{\sigma }(R)$.

38 pages, 4 figures. To appear in Selecta Mathematica

References in corpus (1)

• On moduli of pointed real curves of genus zero