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

Özgür Ceyhan ^[1]
1. [1] University of Montreal
  
  University of Montreal
  
  Canadá
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 2, 2007, págs. 203-237
Idioma: inglés
DOI: 10.1007/s00029-007-0042-8
Enlaces
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Resumen
- 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).