Higher order generalization of Fukaya's Morse homotopy invariant of 3-manifolds II. Invariants of 3-manifolds with $b_1=1$

Abstract

In this paper, it is explained that a topological invariant for 3-manifold $M$ with $b_1(M)=1$ can be constructed by applying Fukaya's Morse homotopy theoretic approach for Chern--Simons perturbation theory to a local system on $M$ of rational functions associated to the free abelian covering of $M$. Our invariant takes values in Garoufalidis--Rozansky's space of Jacobi diagrams whose edges are colored by rational functions. It is expected that our invariant gives a lot of nontrivial finite type invariants of 3-manifolds.

12 pages, 5 figures, typos and an error about self-loop edge corrected

References in corpus (3)

• On the cube of the equivariant linking pairing for knots and 3-manifolds of rank one
• An invariant of fiberwise Morse functions on surface bundle over $S^1$ by counting graphs
• Garoufalidis-Levine's finite type invariants for $\mathbb{Z}\pi$-homology equivalences from 3-manifolds to the 3-torus