Journal of the Ramanujan Mathematical Society

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Equilibrium and Equivariant Triangulations of Some Small Covers With Minimum Number of Vertices


Affiliations
1 Department of Mathematics, Indian Institute of Science, Bangalore-560012, India
2 Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, Regina S4S0A2, Canada
     

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Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal ℤ22-equivariant triangulations of 2-dimensional small covers. We discuss vertex minimal equilibrium triangulations of ℝℙ3#ℝℙ3, S1×ℝℙ2 and a nontrivial S1 bundle over ℝℙ2. We construct some nice equilibrium triangulations of the real projective space ℝℙn with 2n+n+1 vertices. The main tool is the theory of small covers.
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  • Equilibrium and Equivariant Triangulations of Some Small Covers With Minimum Number of Vertices

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Authors

Biplab Basak
Department of Mathematics, Indian Institute of Science, Bangalore-560012, India
Soumen Sarkar
Department of Mathematics and Statistics, University of Regina, 3737 Wascana Parkway, Regina S4S0A2, Canada

Abstract


Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal ℤ22-equivariant triangulations of 2-dimensional small covers. We discuss vertex minimal equilibrium triangulations of ℝℙ3#ℝℙ3, S1×ℝℙ2 and a nontrivial S1 bundle over ℝℙ2. We construct some nice equilibrium triangulations of the real projective space ℝℙn with 2n+n+1 vertices. The main tool is the theory of small covers.