Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braids on surfaces and finite type invariants   We prove that there is no functorial universal finite type invariant for
braids in $\Sigma\times I$ if the genus of $\Sigma$ is positive.

37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph