Contact structures on open 3-manifolds
| dc.creator | Tripp, James | |
| dc.date | 2004-08-03 | |
| dc.date | 2004-09-09 | |
| dc.date.accessioned | 2026-07-07T05:10:59Z | |
| dc.date.available | 2026-07-07T05:10:59Z | |
| dc.description | In this paper, we study contact structures on any open 3-manifold V which is the interior of a compact 3-manifold. To do this, we introduce proper contact isotopy invariants called the slope at infinity and the division number at infinity. We first prove several classification theorems for T^2 x [0, \infty), T^2 x R, and S^1 x R^2 using these concepts. This investigation yields infinitely many tight contact structures on T^2 x [0,\infty), T^2 x R, and S^1 x R^2 which admit no precompact embedding into another tight contact structure on the same space. Finally, we show that if V is irreducible and has an end of nonzero genus, then there are uncountably many tight contact structures on V that are not contactomorphic, yet are isotopic. Similarly, there are uncountably many overtwisted contact structures on V that are not contactomorphic, yet are isotopic. | |
| dc.description | 18 pages, 3 figures, additions to intro, clearer statement of thm 1.1 (same proof), Modifications made to section 6 giving shorter proof of thm 1.2 and 1.3 | |
| dc.identifier | https://arxiv.org/abs/math/0408049 | |
| dc.identifier | http://arxiv.org/abs/math/0408049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72102 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C13; 57M50 | |
| dc.title | Contact structures on open 3-manifolds | |
| dc.type | text |