Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knot signature functions are independent   To each unit complex number with positive imaginary part there is defined a
Tristram-Levine knot signature function. The set of all such signature
functions is linearly independent as a set of functions defined on the set of
all knots. The set of averaged signature functions forms a linearly independent
set of homomorophisms on the knot concordance group. However, for each unit
root of an Alexander polynomial, there is a slice knot with nonvanishing
signature at that root and its conjugate, and nowhere else. These results hold
for knots in all odd dimension.

6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph