#### Volume 5, issue 3 (2005)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear 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
##### 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 $\left(N,\omega \right)$ 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
Primary: 53D20
Secondary: 53D45
##### Publication
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