# 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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