## Topology of spaces of equivariant symplectic embeddings

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- Proc. Amer. Math. Soc.
**135**(2007), 277-288 Request permission

## 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
- MR Author ID: 731609
- Email: apelayo@umich.edu
- 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
- © Copyright 2006 American Mathematical Society
- 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
- MathSciNet review: 2280203