A generalisation of the Morse inequalities


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Bhupal M.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, cilt.70, ss.351-385, 2001 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 70
  • Basım Tarihi: 2001
  • Doi Numarası: 10.1017/s1446788700002391
  • Dergi Adı: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.351-385

Özet

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.