Vol. 263, No. 2, 2013

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(2)3-colorings and right-angled hyperbolic 3-manifolds

Youlin Li and Jiming Ma

Vol. 263 (2013), No. 2, 419–434
Abstract

For a compact 3-manifold N with connected nonempty boundary, let Γ be an admissible trivalent graph in ∂N that decomposes ∂N into a set of disks. As an extension of small covers, from a (2)3-coloring λ on ∂N Γ, one can get a closed 3-manifold Mλ that admits a locally standard (2)3-action.

Suppose N is irreducible and atoroidal: say, a handlebody. We give a combinatorial necessary and sufficient condition for a (2)3-colorable pair (N,Γ) to admit a right-angled hyperbolic structure, which naturally induces a hyperbolic structure on Mλ.

Keywords
(2)3-action, hyperbolic structure with polyhedral boundary, 3-manifold
Mathematical Subject Classification 2010
Primary: 57M50, 57M60
Secondary: 52B70
Milestones
Received: 31 March 2012
Revised: 11 November 2012
Accepted: 25 November 2012
Published: 31 May 2013
Authors
Youlin Li
Department of Mathematics
Shanghai Jiaotong University
200240 Shanghai
China
Jiming Ma
School of Mathematical Sciences
Fudan University
200433 Shanghai
China