2010/09/30 by Janko Latschev, Chris Wendl · 2 citations
Mathematics · #math.SG #math.GT #msc:53D42 #msc:57R17 #msc:53D35 #msc:32Q65
paper · pdf · doi:10.1007/s00039-011-0138-3
published as Geom. Funct. Anal. 21 (2011), no. 5, 1144-1195 · 53 pages, 4 figures, with an appendix by Michael Hutchings; v.3 is a final update to agree with the published paper, and also corrects a minor error that appeared in the published version of the appendix
arxiv created 2012/03/09 · arxiv updated 2012/03/12
We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.