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

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

2006-09-20

arxiv.org/abs/math/0609557v4

Mathematics

Geometric Topology

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

Scientific paper

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 $n\leq 3$, 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.

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