Ohtsuki invariants for integral homology spheres and habiro's cyclotomic expansion

Research output: Contribution to journalArticle

Abstract

We give surgery formulas for the Ohtsuki invariants λ1, λ2 and λ3 of an integral homology sphere obtained by surgery from S3 along a knot, related to Habiro's cyclotomic expansion of the colored Jones polynomial of the knot. As an application, we prove that the Ohtsuki invariants λ1, λ2 and λ3 separate integral homology 3-spheres obtained from S3 by surgery along the Borromean rings.

Original languageEnglish
Pages (from-to)21-31
Number of pages11
JournalJournal of Knot Theory and its Ramifications
Volume18
Issue number1
DOIs
Publication statusPublished - Jan 1 2009
Externally publishedYes

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Homology Spheres
Cyclotomic
Surgery
Knot
Invariant
Borromean rings
Colored Jones Polynomial
Homology

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Ohtsuki invariants for integral homology spheres and habiro's cyclotomic expansion. / Takata, Toshie.

In: Journal of Knot Theory and its Ramifications, Vol. 18, No. 1, 01.01.2009, p. 21-31.

Research output: Contribution to journalArticle

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