Volume 2 (1999)

Download this article
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
About this Series
Editorial Board
Ethics Statement
Submission Guidelines
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Author Index
 
MSP Books and Monographs
Other MSP Publications

Right integrals and invariants of three-manifolds

Louis H Kauffman

Geometry & Topology Monographs 2 (1999) 215–232

DOI: 10.2140/gtm.1999.2.215

Bibliography
1 V G Drinfel'd, Quantum groups, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986)", Amer. Math. Soc. (1987) 798–820 MR934283
2 M Hennings, Invariants of links and 3–manifolds obtained from Hopf algebras, J. London Math. Soc. (2) 54 (1996) 594–624 MR1413901
3 L H Kauffman, Knots and physics, Series on Knots and Everything 1, World Scientific Publishing Co. (1991) MR1141156
4 L H Kauffman, D E Radford, A necessary and sufficient condition for a finite-dimensional Drinfel'd double to be a ribbon Hopf algebra, J. Algebra 159 (1993) 98–114 MR1231205
5 L H Kauffman, D E Radford, Invariants of 3–manifolds derived from finite-dimensional Hopf algebras, J. Knot Theory Ramifications 4 (1995) 131–162 MR1321293
6 L H Kauffman, Hopf algebras and invariants of 3–manifolds, J. Pure Appl. Algebra 100 (1995) 73–92 MR1344844
7 L H Kauffman, D Radford, S Sawin, Centrality and the KRH invariant, J. Knot Theory Ramifications 7 (1998) 571–624 MR1637585
8 L Kauffman, D E Radford, Quantum algebras, quantum coalgebras, invariants of 1–1 tangles and knots, Comm. Algebra 28 (2000) 5101–5156 MR1785491
9 T Kerler, Mapping class group actions on quantum doubles, Comm. Math. Phys. 168 (1995) 353–388 MR1324402
10 R Kirby, A calculus for framed links in S3, Invent. Math. 45 (1978) 35–56 MR0467753
11 R Kirby, P Melvin, The 3–manifold invariants of Witten and Reshetikhin–Turaev for sl(2,C), Invent. Math. 105 (1991) 473–545 MR1117149
12 G Kuperberg, Involutory Hopf algebras and 3–manifold invariants, Internat. J. Math. 2 (1991) 41–66 MR1082836
13 G Kuperberg, Noninvolutory Hopf algebras and 3–manifold invariants, Duke Math. J. 84 (1996) 83–129 MR1394749
14 R G Larson, M E Sweedler, An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math. 91 (1969) 75–94 MR0240169
15 R J Lawrence, A universal link invariant, from: "The interface of mathematics and particle physics (Oxford, 1988)", Inst. Math. Appl. Conf. Ser. New Ser. 24, Oxford Univ. Press (1990) 151–156 MR1103138
16 V V Lyubashenko, Invariants of 3–manifolds and projective representations of mapping class groups via quantum groups at roots of unity, Comm. Math. Phys. 172 (1995) 467–516 MR1354257
17 T Ohtsuki, Invariants of 3–manifolds derived from universal invariants of framed links, Math. Proc. Cambridge Philos. Soc. 117 (1995) 259–273 MR1307080
18 D E Radford, The trace function and Hopf algebras, J. Algebra 163 (1994) 583–622 MR1265853
19 D E Radford, Generalized double crossproducts associated with the quantized enveloping algebras, Comm. Algebra 26 (1998) 241–291 MR1600690
20 D E Radford, On Kauffman's knot invariants arising from finite-dimensional Hopf algebras, from: "Advances in Hopf algebras (Chicago, IL, 1992)", Lecture Notes in Pure and Appl. Math. 158, Dekker (1994) 205–266 MR1289427
21 K Reidemeister, Knotentheorie, Chelsea Publishing Company, New York (1948) MR0345089
22 N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1–26 MR1036112
23 N Y Reshetikhin, Quasitriangular Hopf algebras and invariants of links, Algebra i Analiz 1 (1989) 169–188 MR1025161
24 N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547–597 MR1091619
25 M E Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, New York (1969) MR0252485
26 H Whitney, On regular closed curves in the plane, Compositio Math. 4 (1937) 276–284 MR1556973
27 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351–399 MR990772