Mathematical Research Letters

Volume 18 (2011)

Number 3

Group Width

Pages: 433 – 436



Michael H. Freedman (Microsoft Station Q, University of California at Santa Barbara, CA 93106)


There are many “minimax” complexity functions in mathematics: width of a tree or a link, Heegaard genus of a $3$-manifold, the Cheeger constant of a Riemannian manifold. We define such a function $w$, “width", on countable (or finite) groups and show $w(\mathbb{Z}^k)=k-1$.

Published 20 May 2011