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On the Equivalence Problem for Toric Contact Structures on S-3-Bundles Over S-2
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Pacific Journal of Mathematics, ISSN 0030-8730, Vol. 267, no 2, 277-340 p.Article in journal (Refereed) Published
Abstract [en]

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 show that two toric contact structures with the same first Chern class are contact inequivalent, we use Morse-Bott contact homology. To find inequivalent toric contact structures that are contact equivalent, we show that the corresponding 3-tori belong to distinct conjugacy classes in the contacto-morphism group. We treat a subclass of contact structures which includes the Sasaki-Einstein contact structures Y-p,Y-q studied by physicists with the anti-de Sitter/conformal field theory conjecture. In this case we give a complete solution to the contact equivalence problem by showing that Y-p,Y-q and Y-p',Y-q' are inequivalent as contact structures if and only if p not equal p'.

Place, publisher, year, edition, pages
2014. Vol. 267, no 2, 277-340 p.
Keyword [en]
toric contact geometry, equivalent contact structures, orbifold Hirzebruch surface, contact homology, extremal Sasakian structures
National Category
URN: urn:nbn:se:uu:diva-229535DOI: 10.2140/pjm.2014.267.277ISI: 000338426900002OAI: oai:DiVA.org:uu-229535DiVA: diva2:737101
Available from: 2014-08-11 Created: 2014-08-11 Last updated: 2014-08-11Bibliographically approved

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