Geodesic
$3$-manifolds of small complexity possessing geometries $S^3$ and $Nil$
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 12 (2010), pp. 98-103

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We present lower bounds for the number of closed orientable $3$-manifolds up to complexity $k$ possessing geometries $S^3$ and $Nil$. The bounds are sharp for all $k\leqslant 12$. This allows us to find potentially sharp lower bounds for the number of $3$-manifolds with complexity $13$ possessing geometries $S^3$ and $Nil$.
Keywords: $3$-manifold, complexity, geometric manifold. 
@article{VCHGU_2010_12_a11,
     author = {E. A. Fominykh},
     title = {$3$-manifolds of small complexity possessing geometries $S^3$ and $Nil$},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {98--103},
     publisher = {mathdoc},
     number = {12},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2010_12_a11/}
}
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E. A. Fominykh. $3$-manifolds of small complexity possessing geometries $S^3$ and $Nil$. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 12 (2010), pp. 98-103. http://geodesic.mathdoc.fr/item/VCHGU_2010_12_a11/