This article is cited in 23 papers

Three-Dimensional Manifolds Defined by Coloring a Simple Polytope

I. V. Izmest'ev

M. V. Lomonosov Moscow State University

Abstract: In the present paper we introduce and study a class of three-dimensional manifolds endowed with the action of the group $\mathbb Z_2^3$ whose orbit space is a simple convex polytope. These manifolds originate from three-dimensional polytopes whose faces allow a coloring into three colors with the help of the construction used for studying quasitoric manifolds. For such manifolds we prove the existence of an equivariant embedding into Euclidean space $\mathbb R^4$. We also describe the action on the set of operations of the equivariant connected sum and the equivariant Dehn surgery. We prove that any such manifold can be obtained from a finitely many three-dimensional tori with the canonical action of the group $\mathbb Z_2^3$ by using these operations.

UDC: 515.162.3+515.164.8

Received: 19.06.2000

DOI: 10.4213/mzm511

 English version: Mathematical Notes, 2001, 69:3, 340–346

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