Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Most Refined Invariant of Degree One of Knots and Links in
  $R^1$-Fibrations Over a Surface   As it is well-known, all Vassiliev invariants of degree one of a knot
$K\subset R^3$ are trivial. There are nontrivial Vassiliev invariants of degree
one, when the ambient space is not $R^3$. Recently, T. Fiedler introduced such
invariants of a knot in an $R^1$-fibration over a surface $F$. They take values
in the free $Z$-module generated by all the free homotopy classes of loops in
$F$. Here, we generalize them to the most refined Vassiliev invariant of degree
one. The ranges of values of all these invariants are explicitly described.
  We also construct a similar invariant of a two-component link in an
$\R^1$-fibration. It generalizes the linking number.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom