The Jones representation of genus 2 at the 4th root of unity and the Torelli group

  • Kasahara Y
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Abstract

The linear representation of the mapping class group of a closed orientable surface of genus 2 defined by V. Jones is examined. It arises from the Iwahori-Hecke algebra representations of Artin's braid group of 6 strings. Under a certain nontrivial specialization, the image of the Torelli group is explicitly computed. As an application, the relation with the Rochlin invariant of homology 3-spheres is discussed. © 2001 Elsevier Science B.V. All rights reserved.

Author-supplied keywords

  • Johnson homomorphism
  • Jones representation
  • Mapping class group
  • Torelli group

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Authors

  • Yasushi Kasahara

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