Geodesic
On genus two three-manifolds
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 11 (2009), pp. 105-121

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The paper is devoted to a computer enumeration of genus two Heegaard diagrams and recognition of the corresponding 3-manifolds. Results of computer experiments are presented and a few conjectures are formulated. 
@article{VCHGU_2009_11_a11,
     author = {F. G. Korablev and S. V. Matveev and V. V. Tarkaev},
     title = {On  genus two three-manifolds},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {105--121},
     publisher = {mathdoc},
     number = {11},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2009_11_a11/}
}
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F. G. Korablev; S. V. Matveev; V. V. Tarkaev. On  genus two three-manifolds. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 11 (2009), pp. 105-121. http://geodesic.mathdoc.fr/item/VCHGU_2009_11_a11/