Branched Spines and Contact Structures on 3-manifolds

Details Branched Spines and Contact Structures on 3-manifolds Branched Spines and Contact Structures on 3-manifolds

1998-09-29

arxiv.org/abs/math/9809169v1

Ann. Mat. Pura Appl. (4) 178 (2000), 81-102

Mathematics

Geometric Topology

20 pages, 11 figures

Scientific paper

We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the local existence and uniqueness results which hold for genuine surfaces. Moreover we show that global uniqueness holds when restricting to tight structures. We establish branched versions of the elimination lemma. We prove a smooth version of the Gillman-Rolfsen PL-embedding theorem, deducing that branched spines can be used to construct contact structures in a given homotopy class of plane fields.

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