On the equivalence problem for toric contact structures onS3-bundles overS2

Charles P. Boyer, Justin Pati
2014 Pacific Journal of Mathematics  
We study the contact equivalence problem for toric contact structures on S^3-bundles over S^2. That is, given two toric contact structures, one can ask the question: when are they equivalent as contact structures while inequivalent as toric contact structures? In general this appears to be a difficult problem. To find inequivalent toric contact structures that are contact equivalent, we show that the corresponding 3-tori belong to distinct conjugacy classes in the contactomorphism group. To
more » ... that two toric contact structures with the same first Chern class are contact inequivalent, we use Morse-Bott contact homology. We treat a subclass of contact structures which include the Sasaki-Einstein contact structures Y^p,q studied by physicists. In this subcase we give a complete solution to the contact equivalence problem by showing that Y^p,q and Y^p'q' are inequivalent as contact structures if and only if p≠ p'.
doi:10.2140/pjm.2014.267.277 fatcat:x3cwu47hjrd5lhthildayqgssm