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A duality exact seq...
A duality exact sequence for legendrian contact homology
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- Ekholm, Tobias, 1970- (author)
- Uppsala universitet,Algebra, geometri och logik
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- Etnyre, John (author)
- Department of mathematics, Georgia Tech
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- Sabloff, Josh (author)
- Department of mathematics, Haverford College
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(creator_code:org_t)
- Duke University Press, 2009
- 2009
- English.
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In: Duke mathematical journal. - : Duke University Press. - 0012-7094 .- 1547-7398. ; 150:1, s. 1-75
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Abstract
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- We establish a long exact sequence for Legendrian submanifolds L⊂P×R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L to P off of itself. In this sequence, the singular homology H* maps to linearized contact cohomology CH*, which maps to linearized contact homology CH*, which maps to singular homology. In particular, the sequence implies a duality between Ker(CH*→H*) and CH*/Im(H*). Furthermore, this duality is compatible with Poincaré duality in L in the following sense: the Poincaré dual of a singular class which is the image of a∈CH* maps to a class α∈CH* such that α(a)=1. The exact sequence generalizes the duality for Legendrian knots in R3 (see [26]) and leads to a refinement of the Arnold conjecture for double points of an exact Lagrangian admitting a Legendrian lift with linearizable contact homology, first proved in [7]
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- MATHEMATICS
- MATEMATIK
- Mathematics
- Matematik
Publication and Content Type
- ref (subject category)
- art (subject category)
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