Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A renormalized Riemann-Roch formula and the Thom isomorphism for the
  free loop space
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom