Algebraic and Geometric Topology 5 (2005), paper no. 38, pages 911-922.

The Gromov width of complex Grassmannians

Yael Karshon, Susan Tolman

Abstract. We show that the Gromov width of the Grassmannian of complex k-planes in C^n is equal to one when the symplectic form is normalized so that it generates the integral cohomology in degree 2. We deduce the lower bound from more general results. For example, if a compact manifold N with an integral symplectic form omega admits a Hamiltonian circle action with a fixed point p such that all the isotropy weights at p are equal to one, then the Gromov width of (N,omega) is at least one. We use holomorphic techniques to prove the upper bound.

Keywords. Gromov width, Moser's method, symplectic embedding, complex Grassmannian, moment map

AMS subject classification. Primary: 53D20. Secondary: 53D45.

E-print: arXiv:math.SG/0405391

DOI: 10.2140/agt.2005.5.911

Submitted: 17 September 2004. (Revised: 30 May 2005.) Accepted: 1 June 2005. Published: 3 August 2005.

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Yael Karshon, Susan Tolman
Department of Mathematics, the University of Toronto
Toronto, Ontario, M5S 3G3, Canada
Department of Mathematics, University of Illinois at Urbana-Champaign
1409 W Green St, Urbana, IL 61801, USA

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