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Manifolds associated with $(Z_2)^n$-colored regular graphs by Bao, Zhiqiang; Lü, Zhi is a scholarly article available to read on EtoBox.

What is Manifolds associated with $(Z_2)^n$-colored regular graphs about?

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.

Author

Bao, Zhiqiang; Lü, Zhi

Published

2006

Language

EN