Topology of spaces of equivariant symplectic embeddings

Pelayo, Alvaro

doi:10.1090/S0002-9939-06-08310-9

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 -dimensional ball of some fixed radius into a -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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