The Casson invariant and the word metric on the Torelli group

Nathan Broaddus; Benson Farb; Andrew Putman

doi:10.1016/j.crma.2007.09.018

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arXiv · 0707.2264

The Casson invariant and the word metric on the Torelli group

Nathan Broaddus·Benson Farb·Andrew Putman

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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 $\T$, 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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Nathan Broaddus, Benson Farb, Andrew Putman. 2007-07-16. The Casson invariant and the word metric on the Torelli group. https://doi.org/10.1016/j.crma.2007.09.018

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