Addendum to: "An expansion of the Jones representation of genus 2 and the Torelli group"
Yasushi Kasahara
TL;DR
This paper investigates the determinant of a specific representation related to the Torelli group, revealing restrictions on the structure of certain graded quotients and their trivial summands.
Contribution
It provides new insights into the structure of graded quotients in the Jones representation of genus 2 and the Torelli group, focusing on the implications of the determinant.
Findings
The determinant restricts the structure of the graded quotients.
No trivial 1-dimensional summand exists in these quotients.
Provides an addendum to previous work on the Jones representation.
Abstract
We observe that the determinant of the representation provides a little restriction for the structure of the graded quotients introduced in both [Algebr. Geom. Topol. 1 (2001) 39-55] and [J. Knot Theory Ramifications 13 (2004) 297-306] that any one of them does not contain the trivial 1-dimensional summand.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology