On the LMO Invariant, the Wheeling Theorem, and the Aarhus Integral

TL;DR

This paper explores the relationships between the LMO invariant, the Wheeling Theorem, and the Aarhus integral, building on a generalized framed Kontsevich integral to deepen understanding of these topological invariants.

Contribution

It introduces a generalized framed Kontsevich integral and an isotopy invariant, providing new insights into the construction and interrelations of key topological invariants.

Findings

Established connections between the LMO invariant and the Wheeling Theorem.

Analyzed the properties of the isotopy invariant under band sum moves.

Enhanced understanding of the Aarhus integral's construction.

Abstract

In a previous paper, we generalized the definition of the framed Kontsevich integral initially presented by Le and Murakami. We also defined an isotopy invariant $\widetilde{Z}_f$ that is well-behaved under band sum moves. Using this invariant we study the construction of the LMO invariant, the Wheeling Theorem, and the Aarhus integral.