Manifolds associated with $(Z_2{)}^n$-colored regular graphs

Abstract

In this article we describe a canonical way to expand a certain kind of $({\mathbb{Z}}_2{)}^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\le 3$, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a $({\mathbb{Z}}_2{)}^{n+1}$-colored regular graph admits an $n$-skeletal expansion, then it is realizable as the moment graph of an $(n+1)$-dimensional closed $({\mathbb{Z}}_2{)}^{n+1}$-manifold.

20 pages with 9 figures, in AMS-LaTex, v4 added a new section on reconstructing a space with a $(Z_2{)}^n$-action for which its moment graph is a given colored graph

References in corpus (1)

• Equivariant cohomology and analytic descriptions of ring isomorphisms

Cited by in corpus (1)

• Small covers and the equivariant bordism classification of 2-torus manifolds