#### 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.

Notes on file formats
Yael Karshon, Susan Tolman

Department of Mathematics, the University of Toronto

Toronto, Ontario, M5S 3G3, Canada

and

Department of Mathematics, University of Illinois at Urbana-Champaign

1409 W Green St, Urbana, IL 61801, USA

Email: karshon@math.toronto.edu, stolman@math.uiuc.edu

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