Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite type invariants of nullhomologous knots in 3-manifolds fibered
  over $S^1$ by counting graphs   We study finite type invariants of nullhomologous knots in a closed
3-manifold $M$ defined in terms of certain descending filtration
$\{\mathscr{K}_n(M)\}_{n\geq 0}$ of the vector space $\mathscr{K}(M)$ spanned
by isotopy classes of nullhomologous knots in $M$. The filtration
$\{\mathscr{K}_n(M)\}_{n \geq 0}$ is defined by surgeries on special kinds of
claspers in $M$ having one special leaf. More precisely, when $M$ is fibered
over $S^1$ and $H_1(M)=\mathbb{Z}$, we study how far the natural surgery map
from the space of $\mathbb{Q}[t^{\pm 1}]$-colored Jacobi diagrams on $S^1$ of
degree $n$ to the graded quotient $\mathscr{K}_n(M)/\mathscr{K}_{n+1}(M)$ can
be injective for $n\leq 2$. To do this, we construct a finite type invariant of
nullhomologous knots in $M$ up to degree 2 that is an analogue of the invariant
given in our previous paper arXiv:1503.08735, which is based on Lescop's
construction of $\mathbb{Z}$-equivariant perturbative invariant of 3-manifolds.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph