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2007 Configuration space integral for long $n$–knots and the Alexander polynomial
Tadayuki Watanabe
Algebr. Geom. Topol. 7(1): 47-92 (2007). DOI: 10.2140/agt.2007.7.47


There is a higher dimensional analogue of the perturbative Chern–Simons theory in the sense that a similar perturbative series as in 3 dimensions, which is computed via configuration space integral, yields an invariant of higher dimensional knots (Bott–Cattaneo–Rossi invariant). This invariant was constructed by Bott for degree 2 and by Cattaneo–Rossi for higher degrees. However, its feature is yet unknown. In this paper we restrict the study to long ribbon n–knots and characterize the Bott–Cattaneo–Rossi invariant as a finite type invariant of long ribbon n–knots introduced by Habiro–Kanenobu–Shima. As a consequence, we obtain a nontrivial description of the Bott–Cattaneo–Rossi invariant in terms of the Alexander polynomial.


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Tadayuki Watanabe. "Configuration space integral for long $n$–knots and the Alexander polynomial." Algebr. Geom. Topol. 7 (1) 47 - 92, 2007.


Received: 3 February 2006; Revised: 8 June 2006; Accepted: 12 December 2006; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1133.57016
MathSciNet: MR2289804
Digital Object Identifier: 10.2140/agt.2007.7.47

Primary: 57Q45
Secondary: 57M25

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.7 • No. 1 • 2007
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