Topology of spaces of equivariant symplectic embeddings

Pelayo, Alvaro

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

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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