Bott-Cattaneo-Rossi invariants for long knots in asymptotic homology \mathbb R³

2020/11/08 by Leturcq, David
#55R80 #57K10 #57K14 #57K16 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2011.03926

Abstract

In this article, we express the Alexander polynomial of null-homologous long knots in punctured rational homology 3-spheres in terms of integrals over configuration spaces. To get such an expression, we use a previously established formula, which gives generalized Bott-Cattaneo-Rossi invariants in terms of the Alexander polynomial and vice versa, and we relate these Bott-Cattaneo-Rossi invariants to the perturbative expansion of Chern-Simons theory.

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