Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

One method for finding the Hilbert spaces corresponding to surfaces in Chern-Simons TQFT is by geometrically quantizing the phase space, which is just the character variety of the surface. I know that this has been done by Anderson and others in the holomorphic polarization and by Jeffrey and Weitsman in the real polarization when the gauge group is $SU(2)$.
Is there a derivation of the state spaces for Chern-Simons TQFTs with gauge group $SL(n,\mathbb{C})$ that uses geometric quantization? Equivalently, is there a geometric quantization of the $SL(n,\mathbb{C})$ character varieties of surfaces? Or at least for $n=2$?

share|improve this question

2 Answers 2

This was done in a paper by E. Witten: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1104202513

The paper was written before the arxiv came to be, so unfortunately it is not on the arxiv.

Another paper by Witten may be relevant here: http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.2933v4.pdf but I haven't studied it in detail.

share|improve this answer

The quantization procedure is proposed by Gukov by using A-polynomials


This quantization is shown to be true for $SL(2,\mathbb{C})$ character variety of hyperbolic knots in $S^3$.


share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.