1999/01/25 by Dylan P. Thurston, Thurston, Dylan P. · 5 citations
Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.math/9901110
openalex publication_date 1999/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It has been folklore for several years in the knot theory community that certain integrals on configuration space, originally motivated by perturbation theory for the Chern-Simons field theory, converge and yield knot invariants. This was proposed independently by Gaudagnini, Martellini, and Mintchev and Bar-Natan. The analytic difficulties involved in proving convergence and invariance were reportedly worked out by Bar-Natan, Kontsevich, and Axelrod and Singer. But I know of no elementary exposition of this fact. ... This thesis is an attempt to remedy this lack. I adopt an almost exclusively topological point of view, rarely mentioning Chern-Simons theory. There are also a few new results in this thesis. These include a new construction of the functorial compactification of configuration space (Section 3.2) as well as some variations on the integrals. For a suitable choice of this variation, the integral reduces to counting tinkertoy diagrams (Section 4.5). In particular, the invariants constructed take values in Q.