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Comptes Rendus Mathématique
Volume 345, n° 8
pages 449-452 (octobre 2007)
Doi : 10.1016/j.crma.2007.09.018
Received : 21 July 2007 ;  accepted : 19 September 2007
The Casson invariant and the word metric on the Torelli group
Lʼinvariant de Casson et la métrique des mots sur le groupe de Torelli
 

Nathan Broaddus 1 , Benson Farb 1 , Andrew Putman
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA 

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  , of the element of   associated to any Heegaard splitting of M . We construct examples which show this bound is asymptotically sharp. To cite this article: N. Broaddus et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.
Résumé

Soit M une sphère dʼhomologie de dimension 3. Tout scindement de Heegaard de M définit un élément du groupe de Torelli  . Nous montrons que lʼinvariant de Casson de M est borné par une constante fois le carré de la longueur de cet élément. Cette longueur est définie comme la longueur minimale dʼun mot le représentant, écrit en utilisant un système générateur fini quelconque de  . Nous construisons des exemples qui montrent que cette borne est asymptotiquement la meilleure possible. Pour citer cet article : N. Broaddus et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.
1  Partially supported by the NSF.


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