Geodesic
On projective models of Thurston geometries, some relevant notes on Nil orbifolds and manifolds
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 491-498.

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A unified method is given for describing $3$-orbifolds and $3$-manifolds in terms of a projective interpretation of Thurston geometries. As an application, a new characterization is given for Nil-orbifolds and manifolds arising as fiber spaces over Euclidean $2$-orbifolds with prescribed fundamental groups. (Theorems 3.1–3.2, see also Figure 1).
Keywords: projective spheres, Thurston geometries, Nil-orbifolds and manifolds. 
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E. Molnár. On projective models of Thurston geometries, some relevant notes on Nil orbifolds and manifolds. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 491-498. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a34/

[1] Dunbar W. D., “Geometric orbifolds”, Revista Mat. Univ. Complutense de Madrid, 1:1–3 (1988), 67–99 | MR | Zbl

[2] Kleiner B., and Lott J., “Notes on Perelman's papers”, Geometry Topology, 12 (2008), 2587–2855 Preprint is avialable at, arXiv: math/0605667v3 | DOI | MR | Zbl

[3] Molnár E., “The projective interpretation of the eight $3$-dimensional homogeneous geometries”, Beiträge zur Algebra und Geometrie (Contributions to Algebra and Geometry), 38:2 (1997), 261–288 | MR | Zbl

[4] Molnár E., “Discontinuous groups in homogeneous Riemannian spaces by classification of $D$-symbols”, Publ. Math. Debrecen, 49:3–4 (1996), 265–294 | MR | Zbl

[5] Molnár E., and Papp D., “Visualization of Nil-geometry; Modelling Nil-geometry in Euclidean space with software presentation”, Proc. of Dresden Symposium Geometry – Constructive and Kinematic, 2003, 219–226 | MR | Zbl

[6] Molnár E., Prok I., and Szirmai J., “Classification of tile-transitive 3-simplex tilings and their realizations in homogeneous spaces”, Non-Euclidean Geometries, János Bolyai Memorial Volume, Mathematics and Its Applications, 581, eds. Prekopa A. and Molnár E., Springer, 2005, 321–363 | MR

[7] Molnár E., and Szirmai J., $\mathbf{NIL}$-orbifolds to Euclidean plane group $\mathbf{244}=\mathbf{p4}$, Manuscript, 2005

[8] Molnár E., and Szirmai J., “Symmetries int he 8 homogeneous $3$-geometries”, Symmetry: Culture and Science, (Symmetry Festival 2009, Part 2), 21:1–3 (2010), 87–117

[9] Morgan J. W., “Recent progress on the Poincare conjecture and the classification of $3$-manifolds”, Bulletin (New Series) of the Amer. Math. Soc., 42:1 (2004), 57–78, (Elec. publ. Okt. 2004) | DOI | MR

[10] Perelman G., Finite extinction time for solution to the Ricci flow on certain three-manifolds, July 17. 2003 (May 21. 2006), arXiv: math.DG/0307245

[11] Mir, Moscow, 1986 | DOI | MR | Zbl | Zbl

[12] Szirmai J., “The densest geodesic ball packing by a type of $\mathbf{NIL}$ lattices”, Beiträge zur Algebra und Geometrie (Contributions to Algebra and Geometry), 48:2 (2007), 383–397 | MR | Zbl

[13] Thurston W. P. and Levy S. (eds.), Three-Dimensional Geometry and Topology, v. 1, Princeton University Press, Princeton, New Jersey, 1997 | MR | Zbl