Legendrian intersections in the 1-jet bundle
In this thesis we construct a family of generating functions for a Legendrian embedding, into the I-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 functi...
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ndltd-bl.uk-oai-ethos.bl.uk-3026862017-03-16T15:48:59ZLegendrian intersections in the 1-jet bundleBhupal, Mohan1998In this thesis we construct a family of generating functions for a Legendrian embedding, into the I-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. We also compute the spectral flow of the operator obtained by linearising the gradient equation of the action functional along a path connecting two nondegenerate critical points. We end by making a conjecture about the relation between the Floer connecting orbits and the gradient flow lines of the discrete action functional.510QA MathematicsUniversity of Warwickhttp://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302686http://wrap.warwick.ac.uk/81091/Electronic Thesis or Dissertation |
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510 QA Mathematics |
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510 QA Mathematics Bhupal, Mohan Legendrian intersections in the 1-jet bundle |
description |
In this thesis we construct a family of generating functions for a Legendrian embedding, into the I-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. We also compute the spectral flow of the operator obtained by linearising the gradient equation of the action functional along a path connecting two nondegenerate critical points. We end by making a conjecture about the relation between the Floer connecting orbits and the gradient flow lines of the discrete action functional. |
author |
Bhupal, Mohan |
author_facet |
Bhupal, Mohan |
author_sort |
Bhupal, Mohan |
title |
Legendrian intersections in the 1-jet bundle |
title_short |
Legendrian intersections in the 1-jet bundle |
title_full |
Legendrian intersections in the 1-jet bundle |
title_fullStr |
Legendrian intersections in the 1-jet bundle |
title_full_unstemmed |
Legendrian intersections in the 1-jet bundle |
title_sort |
legendrian intersections in the 1-jet bundle |
publisher |
University of Warwick |
publishDate |
1998 |
url |
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302686 |
work_keys_str_mv |
AT bhupalmohan legendrianintersectionsinthe1jetbundle |
_version_ |
1718421975980834816 |