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

DOI:
https://doi.org/10.1090/S0002-9947-09-04986-1

Published electronically:
October 2, 2009

MathSciNet review:
2563724

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we introduce a relative (or Lagrangian) version of the Seidel homomorphism that assigns to each homotopy class of paths in , starting at the identity and ending on the subgroup that preserves a given Lagrangian submanifold , an element in the Floer homology of . 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:
https://doi.org/10.1090/S0002-9947-09-04986-1

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.