On $p$-adic convergence of perturbative invariants of some rational homology spheres

previous :: next

On $p$-adic convergence of perturbative invariants of some rational homology spheres

L. Rozansky

Source: Duke Math. J. Volume 91, Number 2 (1998), 353-379.

First Page: Show

Primary Subjects: 57N10

Secondary Subjects: 11S80, 57M25

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077232082
Mathematical Reviews number (MathSciNet): MR1600594
Zentralblatt MATH identifier: 0946.57013
Digital Object Identifier: doi:10.1215/S0012-7094-98-09115-3

back to Table of Contents

References

[1] S Akbulut and J. D. McCarthy, Casson's invariant for oriented homology $3$-spheres, Mathematical Notes, vol. 36, Princeton University Press, Princeton, NJ, 1990.

Mathematical Reviews (MathSciNet): MR90k:57017

Zentralblatt MATH: 0695.57011

[2] D. Bar-Natan, Perturbative Chern-Simons theory, J. Knot Theory Ramifications 4 (1995), no. 4, 503–547.

Mathematical Reviews (MathSciNet): MR97c:58157

Zentralblatt MATH: 0861.57009

Digital Object Identifier: doi:10.1142/S0218216595000247

[3] D. Bar-Natan and S. Garoufalidis, On the Melvin-Morton-Rozansky conjecture, Invent. Math. 125 (1996), no. 1, 103–133.

Mathematical Reviews (MathSciNet): MR97i:57004

Zentralblatt MATH: 0855.57004

Digital Object Identifier: doi:10.1007/s002220050070

[4] G. Burde and H. Zieschang, Knots, de Gruyter Studies in Mathematics, vol. 5, Walter de Gruyter & Co., Berlin, 1985.

Mathematical Reviews (MathSciNet): MR87b:57004

Zentralblatt MATH: 0568.57001

[5] D. Freed and R. Gompf, Computer calculation of Witten's $3$-manifold invariant, Comm. Math. Phys. 141 (1991), no. 1, 79–117.

Mathematical Reviews (MathSciNet): MR93d:57027

Zentralblatt MATH: 0739.53065

Digital Object Identifier: doi:10.1007/BF02100006

Project Euclid: euclid.cmp/1104248195

[6] L. Jeffrey, Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation, Comm. Math. Phys. 147 (1992), no. 3, 563–604.

Mathematical Reviews (MathSciNet): MR93f:57042

Zentralblatt MATH: 0755.53054

Digital Object Identifier: doi:10.1007/BF02097243

Project Euclid: euclid.cmp/1104250751

[7] R. Kirby and P. Melvin, The $3$-manifold invariants of Witten and Reshetikhin-Turaev for $\rm sl(2,\bf C)$, Invent. Math. 105 (1991), no. 3, 473–545.

Mathematical Reviews (MathSciNet): MR92e:57011

Zentralblatt MATH: 0745.57006

Digital Object Identifier: doi:10.1007/BF01232277

[8] M. Kontsevich, Vassiliev's knot invariants, I. M. Gel'fand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 137–150.

Mathematical Reviews (MathSciNet): MR94k:57014

Zentralblatt MATH: 0839.57006

[9] R. Lawrence, Asymptotic expansions of Witten-Reshetikhin-Turaev invariants for some simple $3$-manifolds, J. Math. Phys. 36 (1995), no. 11, 6106–6129.

Mathematical Reviews (MathSciNet): MR97a:57015

Zentralblatt MATH: 0877.57008

Digital Object Identifier: doi:10.1063/1.531237

[10] C. Lescop, Invariant de Casson-Walker des sphères d'homologie rationnelle fibrées de Seifert, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 10, 727–730.

Mathematical Reviews (MathSciNet): MR91f:57010

Zentralblatt MATH: 0714.57006

[11] X. S. Lin and Z. Wang, On Ohtsuki's invariants of integral homology spheres, I, preprint, q-alg/9509009.

[12] G. Masbaum and J. Roberts, A simple proof of integrality of quantum invariants at prime roots of unity, Math. Proc. Cambridge Philos. Soc. 121 (1997), no. 3, 443–454.

Mathematical Reviews (MathSciNet): MR98h:57037

Zentralblatt MATH: 0882.57010

Digital Object Identifier: doi:10.1017/S0305004196001624

[13] P. Melvin and H. Morton, The coloured Jones function, Comm. Math. Phys. 169 (1995), no. 3, 501–520.

Mathematical Reviews (MathSciNet): MR96g:57012

Zentralblatt MATH: 0845.57007

Digital Object Identifier: doi:10.1007/BF02099310

Project Euclid: euclid.cmp/1104272852

[14] H. Murakami, Quantum $\rm SU(2)$-invariants dominate Casson's $\rm SU(2)$-invariant, Math. Proc. Cambridge Philos. Soc. 115 (1994), no. 2, 253–281.

Mathematical Reviews (MathSciNet): MR95h:57020

Zentralblatt MATH: 0832.57005

Digital Object Identifier: doi:10.1017/S0305004100072078

[15] H. Murakami, Quantum $\rm SO(3)$-invariants dominate the $\rm SU(2)$-invariant of Casson and Walker, Math. Proc. Cambridge Philos. Soc. 117 (1995), no. 2, 237–249.

Mathematical Reviews (MathSciNet): MR95k:57027

Zentralblatt MATH: 0854.57016

Digital Object Identifier: doi:10.1017/S0305004100073084

[16] T. Ohtsuki, A polynomial invariant of integral homology $3$-spheres, Math. Proc. Cambridge Philos. Soc. 117 (1995), no. 1, 83–112.

Mathematical Reviews (MathSciNet): MR95i:57021

Zentralblatt MATH: 0843.57019

Digital Object Identifier: doi:10.1017/S0305004100072935

[17] T. Ohtsuki, A polynomial invariant of rational homology $3$-spheres, Invent. Math. 123 (1996), no. 2, 241–257.

Mathematical Reviews (MathSciNet): MR97i:57018

Zentralblatt MATH: 0855.57016

[18] N. Reshetikhin and V. Turaev, Invariants of $3$-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991), no. 3, 547–597.

Mathematical Reviews (MathSciNet): MR92b:57024

Zentralblatt MATH: 0725.57007

Digital Object Identifier: doi:10.1007/BF01239527

[19] L. Rozansky, A large $k$ asymptotics of Witten's invariant of Seifert manifolds, Comm. Math. Phys. 171 (1995), no. 2, 279–322.

Mathematical Reviews (MathSciNet): MR96g:57036

Zentralblatt MATH: 0837.57014

Digital Object Identifier: doi:10.1007/BF02099272

Project Euclid: euclid.cmp/1104273564

[20] L. Rozansky, Reshetikhin's formula for the Jones polynomial of a link: Feynman diagrams and Milnor's linking numbers, J. Math. Phys. 35 (1994), no. 10, 5219–5246.

Mathematical Reviews (MathSciNet): MR95i:57013

Zentralblatt MATH: 0824.57006

Digital Object Identifier: doi:10.1063/1.530749

[21]¹ L. Rozansky, A contribution of the trivial connection to the Jones polynomial and Witten's invariant of $3$d manifolds. I, Comm. Math. Phys. 175 (1996), no. 2, 275–296.

Mathematical Reviews (MathSciNet): MR97e:57038

Zentralblatt MATH: 0872.57010

Digital Object Identifier: doi:10.1007/BF02102409

Project Euclid: euclid.cmp/1104275925

[21]² L. Rozansky, A contribution of the trivial connection to the Jones polynomial and Witten's invariant of $3$d manifolds. II, Comm. Math. Phys. 175 (1996), no. 2, 297–318.

Mathematical Reviews (MathSciNet): MR97e:57038

Zentralblatt MATH: 0872.57011

Digital Object Identifier: doi:10.1007/BF02102409

Project Euclid: euclid.cmp/1104275925

[22] L. Rozansky, Residue formulas for the large $k$ asymptotics of Witten's invariants of Seifert manifolds. The case of $\rm SU(2)$, Comm. Math. Phys. 178 (1996), no. 1, 27–60.

Mathematical Reviews (MathSciNet): MR97e:57039

Zentralblatt MATH: 0864.57017

Digital Object Identifier: doi:10.1007/BF02104907

Project Euclid: euclid.cmp/1104286553

[23] L. Rozansky, Witten's invariants of rational homology spheres at prime values of $K$ and trivial connection contribution, Comm. Math. Phys. 180 (1996), no. 2, 297–324.

Mathematical Reviews (MathSciNet): MR98b:57034

Zentralblatt MATH: 0896.57021

Digital Object Identifier: doi:10.1007/BF02099715

Project Euclid: euclid.cmp/1104287350

[24] L. Rozansky, On finite type invariants of links and rational homology spheres derived from the Jones polynomial and Witten-Reshetikhin-Turaev invariant, Geometry and physics (Aarhus, 1995), Lecture Notes in Pure and Appl. Math., vol. 184, Dekker, New York, 1997, pp. 379–397.

Mathematical Reviews (MathSciNet): MR98a:57028

Zentralblatt MATH: 0868.57014

[25] L. Rozansky, Higher order terms in the Melvin-Morton expansion of the colored Jones polynomial, preprint, q-alg/9601009.

Mathematical Reviews (MathSciNet): MR1461960

Zentralblatt MATH: 0882.57004

Digital Object Identifier: doi:10.1007/BF02506408

Project Euclid: euclid.cmp/1158328178

[26] L. Rozansky, The universal $R$-matrix, Burau representation, and the Melvin-Morton expansion of the colored Jones polynomial, preprint, q-alg/9604005.

Mathematical Reviews (MathSciNet): MR1612375

Zentralblatt MATH: 0949.57006

Digital Object Identifier: doi:10.1006/aima.1997.1661

[27] L. Rozansky, in preparation.

[28] K. Walker, An extension of Casson's invariant, Annals of Mathematics Studies, vol. 126, Princeton University Press, Princeton, NJ, 1992.

Mathematical Reviews (MathSciNet): MR93e:57031

Zentralblatt MATH: 0752.57011

[29] E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), no. 3, 351–399.

Mathematical Reviews (MathSciNet): MR90h:57009

Zentralblatt MATH: 0667.57005

Digital Object Identifier: doi:10.1007/BF01217730

Project Euclid: euclid.cmp/1104178138

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?