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A generalisation of the Morse inequalities

Part of: Symplectic geometry, contact geometry Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Mohan Bhupal
Mohan Bhupal
Affiliation:
Mathematics Department Middle East Technical University06531 AnkaraTurkey e-mail: bhupal@math.metu.edu.tr
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Abstract

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In this paper we construct a family of variational families for a Legendrian embedding, into the 1-jet bundle of a closed manifold, that can be obtained from the zero section through Legendrian embdeddings, by discretising the action functional. We compute the second variation of a generating funciton 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 generlisation of the Morse inequalities thus refining a theorem of Chekanov.

MSC classification

Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53D35: Global theory of symplectic and contact manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 3 , June 2001 , pp. 351 - 386
Copyright
Copyright © Australian Mathematical Society 2001

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