The Gromov width of complex Grassmannians

Karshon, Yael; Tolman, Susan

doi:10.2140/agt.2005.5.911

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The Gromov width of complex Grassmannians

Yael Karshon and Susan Tolman

Algebraic & Geometric Topology 5 (2005) 911–922

DOI: 10.2140/agt.2005.5.911

arXiv: math.SG/0405391

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 $ω$ 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 $(N, ω)$ 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

Mathematical Subject Classification 2000

Primary: 53D20

Secondary: 53D45

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Publication

Received: 17 September 2004

Revised: 30 May 2005

Accepted: 1 June 2005

Published: 3 August 2005

Authors

Yael Karshon
Department of Mathematics the University of Toronto Toronto Ontario M5S 3G3 Canada

Susan Tolman
Department of Mathematics University of Illinois at Urbana-Champaign 1409 W Green St Urbana IL 61801 USA

Volume 5, issue 3 (2005)