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2001 An expansion of the Jones representation of genus 2 and the Torelli group
Yasushi Kasahara
Algebr. Geom. Topol. 1(1): 39-55 (2001). DOI: 10.2140/agt.2001.1.39


We study the algebraic property of the representation of the mapping class group of a closed oriented surface of genus 2 constructed by V F R Jones [Annals of Math. 126 (1987) 335-388]. It arises from the Iwahori–Hecke algebra representations of Artin’s braid group of 6 strings, and is defined over integral Laurent polynomials [t,t1]. We substitute the parameter t with eh, and then expand the powers eh in their Taylor series. This expansion naturally induces a filtration on the Torelli group which is coarser than its lower central series. We present some results on the structure of the associated graded quotients, which include that the second Johnson homomorphism factors through the representation. As an application, we also discuss the relation with the Casson invariant of homology 3–spheres.


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Yasushi Kasahara. "An expansion of the Jones representation of genus 2 and the Torelli group." Algebr. Geom. Topol. 1 (1) 39 - 55, 2001.


Received: 18 October 2000; Accepted: 30 November 2000; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0964.57016
MathSciNet: MR1800115
Digital Object Identifier: 10.2140/agt.2001.1.39

Primary: 57N05
Secondary: 20C08, 20F38, 20F40

Rights: Copyright © 2001 Mathematical Sciences Publishers


Vol.1 • No. 1 • 2001
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