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A generalisation of the Morse inequalities
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Date
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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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.