A generalisation of the Morse inequalities
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, vol.70, pp.351-385, 2001 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 70
- Publication Date: 2001
- Doi Number: 10.1017/s1446788700002391
- Journal Name: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.351-385
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: No
Abstract
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.