Resumen de Graph homology of the moduli space of pointed real curves of genus zero

Özgür Ceyhan

• The moduli space Mσ S(R) parameterizes the isomorphism classes of S-pointed stable real curves of genus zero which are invariant under relabeling by the involution σ. This moduli space is stratified according to the degeneration types of σ-invariant curves. The degeneration types of σ-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 Mσ S(R). We show that the homology of Mσ S(R) is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of Mσ S(R).