Journal of the Ramanujan Mathematical Society

Biplab Basak ¹, Soumen Sarkar ²

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

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.

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