Volume 7, issue 1 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Configuration space integral for long $n$–knots and the Alexander polynomial

Tadayuki Watanabe

Algebraic & Geometric Topology 7 (2007) 47–92
Bibliography
1 D Altschuler, L Freidel, Vassiliev knot invariants and Chern–Simons perturbation theory to all orders, Comm. Math. Phys. 187 (1997) 261 MR1463829
2 S Axelrod, I M Singer, Chern–Simons perturbation theory, from: "Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991)", World Sci. Publ., River Edge, NJ (1992) 3 MR1225107
3 D Bar-Natan, Perturbative aspects of the Chern–Simons field theory, PhD thesis, Princeton University (1991)
4 R Bott, Configuration spaces and imbedding invariants, Turkish J. Math. 20 (1996) 1 MR1392659
5 R Bott, C Taubes, On the self-linking of knots, J. Math. Phys. 35 (1994) 5247 MR1295465
6 A S Cattaneo, P Cotta-Ramusino, R Longoni, Configuration spaces and Vassiliev classes in any dimension, Algebr. Geom. Topol. 2 (2002) 949 MR1936977
7 A S Cattaneo, C A Rossi, Wilson surfaces and higher dimensional knot invariants, Comm. Math. Phys. 256 (2005) 513 MR2161270
8 W Fulton, R MacPherson, A compactification of configuration spaces, Ann. of Math. $(2)$ 139 (1994) 183 MR1259368
9 E Guadagnini, M Martellini, M Mintchev, Wilson lines in Chern–Simons theory and link invariants, Nuclear Phys. B 330 (1990) 575 MR1043394
10 K Habiro, T Kanenobu, A Shima, Finite type invariants of ribbon $2$-knots, from: "Low-dimensional topology (Funchal, 1998)", Contemp. Math. 233, Amer. Math. Soc. (1999) 187 MR1701683
11 K Habiro, A Shima, Finite type invariants of ribbon 2–knots II, Topology Appl. 111 (2001) 265 MR1814229
12 T Kohno, Vassiliev invariants and de Rham complex on the space of knots, from: "Symplectic geometry and quantization (Sanda and Yokohama, 1993)", Contemp. Math. 179, Amer. Math. Soc. (1994) 123 MR1319605
13 M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, Vol. II (Paris, 1992)", Progr. Math. 120, Birkhäuser (1994) 97 MR1341841
14 S Poirier, The configuration space integral for links in $\mathbb R^3$, Algebr. Geom. Topol. 2 (2002) 1001 MR1936978
15 C Rossi, Invariants of higher-dimensional knots and topological quantum field theories, PhD thesis, Zurich University (2002)
16 D Thurston, Integral expressions for the Vassiliev knot invariants, AB thesis, Harvard University (1995) arXiv:math.QA/9901110
17 T Watanabe, Clasper-moves among ribbon 2–knots characterizing their finite type invariants, J. Knot Theory Ramifications 15 (2006) 1163
18 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772