2004/08/03 by James Tripp, Tripp, James
Mathematics · #53C13 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:53C13 #msc:57M50
paper · pdf · doi:10.48550/arxiv.math/0408049
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
arxiv created 2004/09/09 · arxiv updated 2009/12/01
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 T2 x [0, ∞), T2 x R, and S1 x R2 using these concepts. This investigation yields infinitely many tight contact structures on T2 x [0,∞), T2 x R, and S1 x R2 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.