Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy ribbon discs with a fixed group   In the topological category, the classification of homotopy ribbon discs is
known when the fundamental group $G$ of the complement is $\mathbb{Z}$ and the
Baumslag-Solitar group $BS(1,2)$. We prove classification results under the
assumption that the group $G$ is good, geometrically $2$-dimensional and
satisfies the Farrell-Jones conjecture. As an application, for any knot $J
\subset S^3$ whose knot group $G(J)$ is good, we classify the homotopy ribbon
discs for $J \# -J$ whose complement has group $G(J)$. A similar application is
obtained for $BS(m,n)$ when $|m-n|=1$.

23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th