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Journal of the Ramanujan Mathematical Society

Volume 30, Issue 1, March 2015  pp. 29–50.

Equilibrium and equivariant triangulations of some small covers with minimum number of vertices

Authors:  Biplab Basak and Soumen Sarkar
Author institution:Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India.

Summary:  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.

Keywords: small cover, triangulation, group action, equivariant triangulation, equilibrium triangulation

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