Skip to main content Accessibility help
×
Home
Hostname: page-component-77ffc5d9c7-zwn4l Total loading time: 0.467 Render date: 2021-04-22T21:00:15.219Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

SO(3) quantum invariants are dense

Published online by Cambridge University Press:  20 November 2009

HELEN WONG
Affiliation:
Dept of Mathematics, Carleton College, 1 North College St Northfield, MN 55057 e-mail: hwong@carleton.edu
Corresponding
E-mail address:

Abstract

We show that when r ≥ 5 is prime, the SO(3) Witten–Reshetikhin–Turaev quantum invariants for three-manifolds at the level r form a dense set in the complex plane. This confirms a conjecture of Larsen and Wang.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2009

Access options

Get access to the full version of this content by using one of the access options below.

References

[1]Blanchet, C.Invariants on three-manifolds with spin structure. Comment. Math. Helv. 67 (1992), 406427.CrossRefGoogle Scholar
[2]Blanchet, C., Habegger, N., Masbaum, G. and Vogel, P.Topological quantum field theories derived from the Kauffman bracket. Topology 34 (1995), 883927.CrossRefGoogle Scholar
[3]Freedman, M., Larsen, M. and Wang, Z.The two-eigenvalue problem and density of Jones representation of braid groups. Commun. Math. Phys. 228 (2002), 177199.CrossRefGoogle Scholar
[4]Freedman, M., Kitaev, A., Larsen, M. and Wang, Z.Topological quantum computation. Bull. Amer. Math. Soc. 40 (2003), 3138.CrossRefGoogle Scholar
[5]Hardy, G. and Wright, E.An Introduction to the Theory of Numbers (Clarendon Press, Oxford Univerity Press, 1979).Google Scholar
[6]Lickorish, W. B. R.Skeins and handlebodies. Pacific J. Math 159 (1993), 337350.CrossRefGoogle Scholar
[7]Lickorish, W. B. R.The skein method for three-manifold invariants. J. Knot Theory Ramifications 2 (1993), no. 2, 171194.CrossRefGoogle Scholar
[8]Lickorish, W. B. R.Quantum invariants of 3-manifolds. Handbook of geometric topology, 707734. (North-Holland, 2002).Google Scholar
[9]Larsen, M. and Wang, Z.Density of the SO(3) TQFT representation of mapping class groups. Commun. Math. Phys. 260 (2005), 641658.CrossRefGoogle Scholar
[10]Masbaum, G. and Roberts, J.On central extensions of mapping class groups. Math. Ann. 302 (1995), no. 1, 131150.CrossRefGoogle Scholar
[11]Roberts, J.Skeins and mapping class groups. Math. Proc. Camb. Phil. Soc. 115 (1994), 5377.CrossRefGoogle Scholar
[12]Roberts, J.Irreducibility of some quantum representations of mapping class groups. Knots in Hellas 1998, Vol. 3 (Delphi). J. Knot Theory Ramifications 10 (2001), no. 5, 763767.CrossRefGoogle Scholar
[13]Reshetikhin, R. and Turaev, V.Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103 (1991), 547597.CrossRefGoogle Scholar
[14]Turaev, V.Quantum invariants of knots and 3-manifolds. de Gruyter Studies in Mathematics, 18 (Walter de Gruyter & Co., 1994.)Google Scholar
[15]Witten, E.Quantum field theory and the Jones polynomial. Commun. Math. Phys. 121 (1989), 351399.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 21 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 22nd April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

SO(3) quantum invariants are dense
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

SO(3) quantum invariants are dense
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

SO(3) quantum invariants are dense
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *