Volume 5, issue 3 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The Gromov width of complex Grassmannians

Yael Karshon and Susan Tolman

Algebraic & Geometric Topology 5 (2005) 911–922

arXiv: math.SG/0405391


We show that the Gromov width of the Grassmannian of complex k–planes in 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.

Gromov width, Moser's method, symplectic embedding, complex Grassmannian, moment map
Mathematical Subject Classification 2000
Primary: 53D20
Secondary: 53D45
Forward citations
Received: 17 September 2004
Revised: 30 May 2005
Accepted: 1 June 2005
Published: 3 August 2005
Yael Karshon
Department of Mathematics
the University of Toronto
Ontario M5S 3G3
Susan Tolman
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green St
Urbana IL 61801