The PSU(3) invariant of the Poincaré homology sphere

Ruth Lawrence

doi:10.1016/S0166-8641(02)00057-3

The PSU(3) invariant of the Poincaré homology sphere

Ruth Lawrence^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 language	English
Pages (from-to)	153-168
Number of pages	16
Journal	Topology and its Applications
Volume	127
Issue number	1-2
DOIs	https://doi.org/10.1016/S0166-8641(02)00057-3
State	Published - 1 Jan 2003

Bibliographical note

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

Keywords

Ohtsuki series
Pertubative invariant
Quantum groups
Quantum topology

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10.1016/S0166-8641(02)00057-3

Cite this

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title = "The PSU(3) invariant of the Poincar{\'e} homology sphere",

abstract = "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 Poincar{\'e} 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 Poincar{\'e} homology sphere, which it was shown by Thang Le could be extracted from the PSU(N) invariants of any rational homology sphere.",

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N2 - 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.

AB - 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.

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KW - Pertubative invariant

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The PSU(3) invariant of the Poincaré homology sphere

Abstract

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Keywords

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