A generalisation of the Morse inequalities

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2001-06-01

Author

Bhupal, Mohan Lal

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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 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.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/47447

Journal

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS

DOI

https://doi.org/10.1017/s1446788700002391

Collections

Department of Mathematics, Article

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Citation Formats

M. L. Bhupal, “A generalisation of the Morse inequalities,” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, pp. 351–385, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47447.