The Casson invariant and the word metric on the Torelli group (with N. Broaddus and B. Farb) - [pdf] [ps]
C. R. Acad. Sci. Paris, Ser. I 345 (2007) 449-452.

Abstract :
We bound the value of the Casson invariant of any integral homology 3-sphere $M$ by a constant times the distance-squared to the identity, measured in any word metric on the Torelli group $\mathcal{I}$, of the element of $\mathcal{I}$ associated to any Heegaard splitting of $M$. We construct examples which show this bound is asymptotically sharp.