Geodesic
Fundamental Groups of Three-Dimensional Small Covers
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Tome 317 (2022), pp. 89-106

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Small covers arising from three-dimensional simple polytopes are an interesting class of 3-manifolds. The fundamental group is a rigid invariant for wide classes of 3-manifolds, particularly for orientable Haken manifolds, which include orientable small covers over flag polytopes. By using the Morse-theoretic approach, we give a procedure to get an explicit balanced presentation of the fundamental group of a closed orientable three-dimensional small cover with minimal number of generators. Our procedure is completely algorithmic and geometrical.
Keywords: fundamental group, Haken manifold, three-dimensional simple polytope. 
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     author = {Vladimir Gruji\'c},
     title = {Fundamental {Groups} of {Three-Dimensional} {Small} {Covers}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {89--106},
     publisher = {mathdoc},
     volume = {317},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_317_a3/}
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Vladimir Grujić. Fundamental Groups of Three-Dimensional Small Covers. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Tome 317 (2022), pp. 89-106. http://geodesic.mathdoc.fr/item/TM_2022_317_a3/