Geodesic
Action of free commuting involutions on closed two-dimensional manifolds
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2021), pp. 44-47

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Consider a function $f(g)$ associating each oriented surface $M$ of genus $g$ with the maximal number of free commuting involutions on $M$. It is proved that the surface of minimal genus $g$ for which $f(g) = n$ is the moment-angle complex $\mathcal{R}_\mathcal{K}$, where $\mathcal K$ is the boundary of an $(n+2)$-gon. Its genus is given by the formula $g=1+2^{n-1}(n-2)$. 
@article{VMUMM_2021_4_a7,
     author = {T. Yu. Neretina},
     title = {Action of free commuting involutions on closed two-dimensional manifolds},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {44--47},
     publisher = {mathdoc},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_4_a7/}
}
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T. Yu. Neretina. Action of free commuting involutions on closed two-dimensional manifolds. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2021), pp. 44-47. http://geodesic.mathdoc.fr/item/VMUMM_2021_4_a7/