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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 317, Pages 89–106
DOI: https://doi.org/10.4213/tm4293 (Mi tm4293) 		 
Fundamental Groups of Three-Dimensional Small Covers

Vladimir Grujić

Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia
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DOI: https://doi.org/10.4213/tm4293
Abstract: 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.
Funding agency Grant number
Science Fund of the Republic of Serbia 7744592
This research was supported by the Science Fund of the Republic of Serbia, grant no. 7744592, Integrability and Extremal Problems in Mechanics, Geometry and Combinatorics – MEGIC.
Received: March 31, 2022
Revised: June 14, 2022
Accepted: June 16, 2022
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 317, Pages 78–93
DOI: https://doi.org/10.1134/S0081543822020043
Bibliographic databases:
Document Type: Article
UDC: 515.162.3
Language: Russian
Citation: Vladimir Grujić, “Fundamental Groups of Three-Dimensional Small Covers”, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Collected papers, Trudy Mat. Inst. Steklova, 317, Steklov Math. Inst., М., 2022, 89–106; Proc. Steklov Inst. Math., 317 (2022), 78–93
Citation in format AMSBIB
\Bibitem{Gru22}
\by Vladimir~Gruji\'c
\paper Fundamental Groups of Three-Dimensional Small Covers
\inbook Toric Topology, Group Actions, Geometry, and Combinatorics. Part~1
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 317
\pages 89--106
\publ Steklov Math. Inst.
\publaddr М.
\mathnet{http://mi.mathnet.ru/tm4293}
\crossref{https://doi.org/10.4213/tm4293}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538824}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 317
\pages 78--93
\crossref{https://doi.org/10.1134/S0081543822020043}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85141988214}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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