Geodesic
Moduli spaces $\mathcal{M}_{2,1}$ and $\mathcal{M}_{3,1}$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 48-56

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The cell structure of the spaces $\mathcal{M}_{2,1}$ and $\mathcal{M}_{3,1}$ is considered. These are the spaces of complex curves of genus 2 and 3 with one marked point. For the space $\mathcal{M}_{2,1}$, nine cells of the highest dimension 8 are described and their adjacency is studied. For the space $\mathcal{M}_{3,1}$, a list of all $1726$ cells of the highest dimension 14 (with orientation) is obtained. The list of adjacent couples of cells is also obtained. These lists can be found on the web.
Keywords: moduli space of curves with marked points, embedded graphs. 
@article{FAA_2010_44_2_a4,
     author = {Yu. Yu. Kochetkov},
     title = {Moduli spaces $\mathcal{M}_{2,1}$ and $\mathcal{M}_{3,1}$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {48--56},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a4/}
}
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Yu. Yu. Kochetkov. Moduli spaces $\mathcal{M}_{2,1}$ and $\mathcal{M}_{3,1}$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 44 (2010) no. 2, pp. 48-56. http://geodesic.mathdoc.fr/item/FAA_2010_44_2_a4/