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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A relative Seidel morphism and the Albers map


Authors: Shengda Hu and François Lalonde
Journal: Trans. Amer. Math. Soc. 362 (2010), 1135-1168
MSC (2000): Primary 53D12, 53D40, 53D45, 57R58, 57S05
Published electronically: October 2, 2009
MathSciNet review: 2563724
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Abstract: In this note, we introduce a relative (or Lagrangian) version of the Seidel homomorphism that assigns to each homotopy class of paths in $ {\rm Ham}(M)$, starting at the identity and ending on the subgroup that preserves a given Lagrangian submanifold $ L$, an element in the Floer homology of $ L$. We show that these elements are related to the absolute Seidel elements by the Albers map. We also study, for later use, the effect of reversing the signs of the symplectic structure as well as the orientations of the generators and of the operations on the Floer homologies.


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Additional Information

Shengda Hu
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada
Email: hshengda@math.uwaterloo.ca

François Lalonde
Affiliation: Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada
Email: lalonde@dms.umontreal.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04986-1
PII: S 0002-9947(09)04986-1
Received by editor(s): September 27, 2006
Published electronically: October 2, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.