# Topology of spaces of equivariant symplectic embeddings

## TL;DR

This paper determines the homotopy type of the space of equivariant symplectic embeddings into symplectic-toric manifolds and introduces an invariant based on this topology.

## Contribution

It computes the homotopy type of equivariant embedding spaces and defines a new invariant for symplectic-toric manifolds.

## Key findings

- Homotopy type of equivariant embedding space computed
- A Z-valued step function invariant is introduced
- Results extend to partially equivariant cases

## Abstract

We compute the homotopy type of the space of T^n-equivariant symplectic embeddings from the standard 2n-dimensional ball of some fixed radius into a 2n-dimensional symplectic-toric manifold M, and use this computation to define a Z-valued step function on the positive real line which is an invariant of the symplectic-toric type of M. We conclude with a discussion of the partially equivariant case of this result.