Higher order generalization of Fukaya's Morse homotopy invariant of 3-manifolds II. Invariants of 3-manifolds with b₁=1

2016/05/18 by Tadayuki Watanabe, Watanabe, Tadayuki
Mathematics · #57M27 #57R57 #58D29 #58E05 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1605.05620

openalex publication_date 2016/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, it is explained that a topological invariant for 3-manifold M with b₁(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.

Citations

• Garoufalidis-Levine's finite type invariants for ℤπ-homology equivalences from 3-manifolds to the 3-torus

Related

• Higher order generalization of Fukaya's Morse homotopy invariant of 3-manifolds I. Invariants of homology 3-spheres
• Garoufalidis-Levine's finite type invariants for ℤπ-homology equivalences from 3-manifolds to the 3-torus
• The space of 3-manifolds and Vassiliev finite-type invariants
• On Vassiliev knot invariants induced from finite type 3-manifold invariants
• On perturbative invariants of combed three-manifolds