Bhupal, Mohan (1998) Legendrian intersections in the 1-jet bundle. PhD thesis, University of Warwick.

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Abstract

In this thesis we construct a family of generating functions for a Legendrian embedding, into the I-jet bundle of a closed manifold, that can be obtained from the zero section through Legendrian embeddings, by discretising the action functional. We compute the second variation of a generating function obtained as above at a nondegenerate critical point and prove a formula relating the signature of the second variation to the Maslov index as the mesh goes to zero. We use this to prove a generalisation of the Morse inequalities thus refining a theorem of Chekanov. We also compute the spectral flow of the operator obtained by linearising the gradient equation of the action functional along a path connecting two nondegenerate critical points. We end by making a conjecture about the relation between the Floer connecting orbits and the gradient flow lines of the discrete action functional.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Manifolds (Mathematics)
Official Date:	1998
Dates:	Date Event 1998 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Salamon, Dietar
Extent:	v, 77 leaves
Language:	eng

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