On converting a side-pairing to a handle decomposition

2008/10/22 by Dubravko Ivanšić, Ivanšić, Dubravko
Mathematics · #57M25 #57M50 #57Q45 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57M50 #msc:57Q45

paper · pdf · doi:10.48550/arxiv.0810.4183

arxiv created 2008/10/22 · arxiv updated 2009/12/01

Abstract

We give a method for obtaining a handle decomposition of an n-manifold if the manifold is given by isometric side-pairings of a polyhedron in \en, \sn or \hn. Every cycle of k-faces on the polyhedron corresponds to an (n-k)-handle of the manifold. Two applications of the method are given. One helps recognize when a noncompact hyperbolic 3-manifold is a complement of a link in S³ (and automatically produces the link diagram), the other shows that a topological S⁴ described by the author in \citeIvansic3 is diffeomorphic to the standard differentiable S⁴.

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