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.
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Acknowledgments
The author is very grateful to the referee for carefully reading the paper and making constructive suggestions which significantly improved the exposition of the main result.
Funding
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.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Vol. 317, pp. 89–106 https://doi.org/10.4213/tm4293.
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Grujić, V. Fundamental Groups of Three-Dimensional Small Covers. Proc. Steklov Inst. Math. 317, 78–93 (2022). https://doi.org/10.1134/S0081543822020043
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DOI: https://doi.org/10.1134/S0081543822020043