The PSU(3) invariant of the Poincaré homology sphere

Ruth Lawrence*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Using the R-matrix formulation of the sl3 invariant of links, we compute the coloured sl3 generalised Jones polynomial for the trefoil. From this, the PSU(3) invariant of the Poincaré homology sphere is obtained. This takes complex number values at roots of unity. The result obtained is formally an infinite sum, independent of the order of the root of unity, which at roots of unity reduces to a finite sum. This form enables the derivation of the PSU(3) analogue of the Ohtsuki series for the Poincaré homology sphere, which it was shown by Thang Le could be extracted from the PSU(N) invariants of any rational homology sphere.

Original languageAmerican English
Pages (from-to)153-168
Number of pages16
JournalTopology and its Applications
Issue number1-2
StatePublished - 1 Jan 2003

Bibliographical note

Funding Information:
✩ Partially supported by a Guastella Fellowship and by BSF Grant 1998119. E-mail address: (R. Lawrence).


  • Ohtsuki series
  • Pertubative invariant
  • Quantum groups
  • Quantum topology


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