Geodesic
Homologies of moduli space $\mathcal M_{2,1}$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 45-63
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We consider the open moduli space $\mathcal M_{2,1}$ of complex curves of genus 2 with one marked point. Using the language of chord diagrams, we describe the cell structure of $\mathcal M_{2,1}$ and cell adjacency. This allows us to construct matrices of boundary operators and compute Betty numbers of $\mathcal M_{2,1}$ over $\mathbb Q$. 
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Yu. Yu. Kochetkov. Homologies of moduli space $\mathcal M_{2,1}$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 45-63. http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a4/

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