Some computations of Ohtsuki series

N Jacoby, R Lawrence

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present some computational data on Ohtsuki series for a two parameter family of integer homology spheres obtained by surgery around what we call ‘2–strand knots’, closures of the simplest rational tangles. This data allows us to make certain conjectures about the growth rate of the coefficients in Ohtsuki series generally, based on which we introduce an invariant which we call the slope σ(M) of a manifold M (not to be confused with slopes in hyperbolic geometry). For Seifert fibred manifolds, M, the conjectures are known to hold while π2σ(M) Î Q; furthermore if M is also an integer homology sphere, π2σ(M) Î Z. Assuming the conjectures, the numerical data enables us to give an example of a ZHS for which π2σ(M) Ï Z.
Original languageEnglish
Title of host publicationAdvances in Topological Quantum Field Theory
Subtitle of host publicationProceedings of the NATO Advanced Research Workshop on New Techniques in Topological Quantum Field Theory, Kananaskis Village, Canada 22 - 26 August 2001
EditorsJohn M. Bryden
PublisherSpringer-Verlag
Pages53-70
Number of pages18
ISBN (Electronic)978-1-4020-2772-7
ISBN (Print)978-1-4020-2770-3, 978-1-4020-2771-0
DOIs
StatePublished - 2004
EventNATO Advanced Research Workshop on New Techniques in Topological Quantum Field Theory - Kananaskis Village, Canada
Duration: 22 Aug 200126 Aug 2001

Publication series

NameNATO Science Series II: Mathematics, Physics and Chemistry
PublisherSpringer
Volume179
ISSN (Print)1568-2609

Conference

ConferenceNATO Advanced Research Workshop on New Techniques in Topological Quantum Field Theory
Country/TerritoryCanada
CityKananaskis Village
Period22/08/0126/08/01

Bibliographical note

This paper is based on the first author’s M.Sc. thesis.

Keywords

  • Ohtsuki series
  • Seifert fibred manifold
  • Quantum invariants
  • Rational tangle

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