Combinatorial constructions of three-dimensional small covers

Yasuzo Nishimura

Vol. 256 (2012), No. 1, 177–199

DOI: 10.2140/pjm.2012.256.177

Abstract

We study two operations on 3-dimensional small covers called connected sum and surgery. These operations correspond to combinatorial operations on (ℤ₂)³-colored simple convex polytopes. Then we show that each 3-dimensional small cover can be constructed from T³, ℝP³ and S¹ × ℝP² with two different (ℤ₂)³-actions by using these operations. This is a generalization of the results of Izmest’ev and Nishimura, and an improvement of the results of Kuroki and Lü and Yu.

Keywords

small cover, equivariant surgery, connected sum, 3-polytope

Mathematical Subject Classification 2010

Primary: 57M50, 57M60, 57S17

Secondary: 52B10

Milestones

Received: 5 April 2011

Revised: 28 March 2012

Accepted: 10 April 2012

Published: 6 May 2012