Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable Commutator Length in Amalgamated Free Products   We show that stable commutator length is rational on free products of free
Abelian groups amalgamated over $\mathbb{Z}^k$, a class of groups containing
the fundamental groups of all torus knot complements. We consider a geometric
model for these groups and parameterize all surfaces with specified boundary
mapping to this space. Using this work we provide a topological algorithm to
compute stable commutator length in these groups. Further, we use the methods
developed to show that in free products of cyclic groups the stable commutator
length of a fixed varies quasirationally in the orders of the free factors.

35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin