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We give a generalization of Fukayas Morse homotopy theoretic approach for 2-loop Chern--Simons perturbation theory to 3-valent graphs with arbitrary number of loops at least 2. We construct a sequence of invariants of integral homology 3-spheres with values in a space of 3-valent graphs (Jacobi diagrams or Feynman diagrams) by counting graphs in an integral homology 3-sphere satisfying certain condition described by a set of ordinary differential equations.
In this paper, it is explained that a topological invariant for 3-manifold $M$ with $b_1(M)=1$ can be constructed by applying Fukayas Morse homotopy theoretic approach for Chern--Simons perturbation theory to a local system on $M$ of rational functio
Garoufalidis and Levine defined a filtration for 3-manifolds equipped with some degree 1 map ($mathbb{Z}pi$-homology equivalence) to a fixed 3-manifold $N$ and showed that there is a natural surjection from a space of $pi=pi_1N$-decorated graphs to t
We define an invariant of rational homology 3-spheres via vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston invariant and that of Watanabes Morse homotopy invariant, which implies the equivalence of these two invariants.
We study a theory of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Goussarov-Rozansky theory for
We study finite type invariants of nullhomologous knots in a closed 3-manifold $M$ defined in terms of certain descending filtration ${mathscr{K}_n(M)}_{ngeq 0}$ of the vector space $mathscr{K}(M)$ spanned by isotopy classes of nullhomologous knots i