Math Papers

---

A Morse-Bott approach to contact homology
Ph.D. Thesis, Stanford University, 2002.

---

Contact homology was introduced by Eliashberg, Givental and Hofer. In this theory, we count holomorphic curves in the symplectization of a contact manifold, which are asymptotic to periodic Reeb orbits. These closed orbits are assumed to be nondegenerate and, in particular, isolated. This assumption makes practical computations of contact homology very difficult.
In this thesis, we develop computational methods for contact homology in Morse-Bott situations, in which closed Reeb orbits form submanifolds of the contact manifold. We require some Morse-Bott type assumptions on the contact form, a positivity property for the Maslov index, mild requirements on the Reeb flow, and c₁(ξ) = 0.
We then use these methods to compute contact homology for several examples, in order to illustrate their efficiency. As an application of these contact invariants, we show that T⁵ and T² × S³ carry infinitely many pairwise non-isomorphic contact structures in the trivial formal homotopy class.

---

You can download the full text of my Ph.D. thesis in PostScript or in PDF format.

---

Back