Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0608324

SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial

Sergei Gukov·Hitoshi Murakami
View original source ↗Read source document ↗Export metadata ↓

Abstract

We clarify and refine the relation between the asymptotic behavior of the colored Jones polynomial and Chern-Simons gauge theory with complex gauge group SL(2,C). The precise comparison requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern-Simons theory. Addressing these issues allows us to go beyond the volume conjecture and to verify some predictions for the behavior of the subleading terms in the asymptotic expansion of the colored Jones polynomial.

Explore related subjects

math.GThep-thmath.QA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sergei Gukov, Hitoshi Murakami. 2007-06-19. SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial. https://doi.org/10.1007/s11005-008-0282-3

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The mod 2 Seiberg-Witten invariants of spin structures and spin families

We completely determine the mod $2$ Seiberg-Witten invariants for any spin structure on any closed, oriented, smooth $4$-manifold $X$. Our computation confirms the validity of the simple type conjecture mod $2$ for spin structures. Our proof also works for families of spin $4$-manifolds and thus computes the mod $2$ Seiberg-Witten invariants for spin families. The proof of our main result uses $Pin(2)$-symmetry to define an enhancement of the mod $2$ Seiberg-Witten invariants. We prove a connected sum formula for the enhanced invariant using localisation in equivariant cohomology. Unlike the usual Seiberg-Witten invariant, the enhanced invariant does not vanish on taking connected sums and by exploiting this property, we are able to compute the enhanced invariant.

math.GT↗
arXiv2026

Isotopy versus equivariant isotopy in dimensions three and higher

Given a finite group action on a smooth manifold, we study the following question: if two equivariant diffeomorphisms are isotopic, must they be equivariantly isotopic? Birman-Hilden and Maclachlan-Harvey proved the answer is "yes" for most surfaces. By contrast, we give a general criterion in higher dimensions under which there are many equivariant diffeomorphisms which are isotopic but not equivariantly isotopic. Examples satisfying this criterion include branched covers of split links and "stabilized" branched covers. We prove the result by constructing an invariant valued in the homology of a certain infinite cover of the manifold. We give applications to outer automorphism groups of free products and to group actions on manifolds which fiber over the circle.

math.GT↗