60 research outputs found
Open books for contact five-manifolds and applications of contact homology
In the first half of this thesis, we use Giroux's construction of contact open books to construct contact structures on simply connected five-manifolds. This allows us to reprove a theorem of Geiges concerning the existence of contact structures in all homotopy classes of almost contact structures on simply-connected five-manifolds. In the second part of this thesis, we give an algorithm for computing the contact homology of some Brieskorn manifolds. As an application, we construct infinitely many contact structures on the class of simply connected contact manifolds that admit nice contact forms (i.e. no Reeb orbits of degree -1, 0 or 1) and have index positivity with trivial first Chern class. In particular we give examples of simply connected five-manifolds with infinitely many contact structures
Contact homology of Brieskorn manifolds
We give an algorithm for computing the contact homology of some Brieskorn
manifolds. As an application, we construct infinitely many contact structures
on the class of simply connected contact manifolds that admit nice contact
forms (i.e. no Reeb orbits of degree -1,0 or 1) and have index positivity with
trivial first Chern class.Comment: 20 pages; corrected typos, added some explanations in section 2.3; to
appear in Forum Mathematicu
Open books on contact five-manifolds
The aim of this paper is to give an alternative proof of a theorem about the
existence of contact structures on five-manifolds due to Geiges. This theorem
asserts that simply-connected five-manifolds admit a contact structure in every
homotopy class of almost contact structures. Our proof uses the open book
construction of Giroux.Comment: 15 pages, 2 figures; typos corrected, used simpler argument for
section 3; to appear in Annales de l'institut Fourie
Open book decompositions for contact structures on Brieskorn manifolds
In this paper, we give an open book decomposition for the contact structures
on some Brieskorn manifolds, in particular for the contact structures of
Ustilovsky. The decomposition uses right-handed Dehn twists as conjectured by
Giroux.Comment: 6 pages, no figure
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