The homotopy type of the space of symplectic balls in S² × S² above the critical value

2004/06/07 by Sylvia Anjos, Anjos, Sylvia, Francois Lalonde +1
Mathematics · #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG

paper · pdf · doi:10.48550/arxiv.math/0406129

The paper has been revised; the main change concerns the computation of the differential of the element of degree 4 in the minimal model of the space of non-parametrized embedded symplectic balls

arxiv created 2007/07/04 · arxiv updated 2009/12/01

Abstract

We compute in this note the full homotopy type of the space of symplectic embeddings of the standard ball B⁴(c) ⊂ \R⁴ (where c= πr² is the capacity of the standard ball of radius r) into the 4-dimensional rational symplectic manifold M_μ= (S² × S², μ\om₀ ⊕ \om₀) where \om₀ is the area form on the sphere with total area 1 and μ belongs to the interval (1,2]. We know, by the work of Lalonde-Pinsonnault, that this space retracts to the space of symplectic frames of M_μ for any value of c smaller than the critical value μ-1, and that its homotopy type does change when c crosses that value. In this paper, we compute the homotopy type for the case c ≥ μ-1 and prove that it is not the type of a finite CW-complex.

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• Symplectic packing in dimension 4
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