Graph homology of the moduli space of pointed real curves of genus zero期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Özgür Ceyhan

Institution:	(1) Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada

Abstract:	The moduli space $\overline{M}^{\sigma}_{\bf S}({\mathbb{R}})$ 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 $\overline{M}^{\sigma}_{\bf S}({\mathbb{R}})$ . We show that the homology of $\overline{M}^{\sigma}_{\bf S}({\mathbb{R}})$ is isomorphic to the homology of our graph complex. We also give a presentation of the fundamental group of $\overline{M}^{\sigma}_{\bf S}({\mathbb{R}})$ .

Keywords:	Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 14Dxx Secondary 14P25
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