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Topology of spaces of equivariant symplectic embeddings


Author: Alvaro Pelayo
Journal: Proc. Amer. Math. Soc. 135 (2007), 277-288
MSC (2000): Primary 53D20; Secondary 53D05
DOI: https://doi.org/10.1090/S0002-9939-06-08310-9
Published electronically: July 28, 2006
MathSciNet review: 2280203
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Abstract: We compute the homotopy type of the space of $ \mathbb{T}^n$-equivariant symplectic embeddings from the standard $ 2n$-dimensional ball of some fixed radius into a $ 2n$-dimensional symplectic-toric manifold $ (M, \, \sigma)$, and use this computation to define a $ \mathbb{Z}_{\ge 0}$-valued step function on $ \mathbb{R}_{\ge 0}$ which is an invariant of the symplectic-toric type of $ (M, \, \sigma)$. We conclude with a discussion of the partially equivariant case of this result.


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Additional Information

Alvaro Pelayo
Affiliation: Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, Michigan 48109-1043
Email: apelayo@umich.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08310-9
Received by editor(s): August 5, 2004
Received by editor(s) in revised form: April 22, 2005
Published electronically: July 28, 2006
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2006 American Mathematical Society

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