The Casson invariant and the word metric on the Torelli group

Details The Casson invariant and the word metric on the Torelli group The Casson invariant and the word metric on the Torelli group

2007-07-16

arxiv.org/abs/0707.2264v2

C. R. Acad. Sci. Paris, Ser. I 345 (2007) 449--452.

Mathematics

Geometric Topology

5 pages, minor corrections; to appear in C. R. Math. Acad. Sci. Paris

Scientific paper

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 $\T$, of the element of $\T$ associated to any
Heegaard splitting of $M$. We construct examples which show this bound is
asymptotically sharp.

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