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A Morse-Bott approach to contact hom...

Bourgeois, Frederic.

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A Morse-Bott approach to contact homology.

Record Type:	Electronic resources : Monograph/item
Title/Author:	A Morse-Bott approach to contact homology./
Author:	Bourgeois, Frederic.
Description:	123 p.
Notes:	Source: Dissertation Abstracts International, Volume: 63-04, Section: B, page: 1872.
Contained By:	Dissertation Abstracts International63-04B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3048497
ISBN:	0493628282

A Morse-Bott approach to contact homology.
Bourgeois, Frederic.

A Morse-Bott approach to contact homology. - 123 p.

Source: Dissertation Abstracts International, Volume: 63-04, Section: B, page: 1872.

Thesis (Ph.D.)--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.

ISBN: 0493628282Subjects--Topical Terms:

515831
Mathematics.

A Morse-Bott approach to contact homology.
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100 1 $a Bourgeois, Frederic. $3 1941666
245 1 0 $a A Morse-Bott approach to contact homology.
300 $a 123 p.
500 $a Source: Dissertation Abstracts International, Volume: 63-04, Section: B, page: 1872.
500 $a Adviser: Yakov Eliashberg.
502 $a Thesis (Ph.D.)--Stanford University, 2002.
520 $a 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.
520 $a 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 <italic>c</italic><sub>1</sub>(ξ) = 0.
520 $a 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 <italic>T</italic><super>5</super> and <italic>T </italic><super>2</super> × <italic>S</italic><super>3</super> carry infinitely many pairwise non-isomorphic contact structures in the trivial formal homotopy class.
590 $a School code: 0212.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a Stanford University. $3 754827
773 0 $t Dissertation Abstracts International $g 63-04B.
790 1 0 $a Eliashberg, Yakov, $e advisor
790 $a 0212
791 $a Ph.D.
792 $a 2002
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3048497