Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Unknotting Problem and Normal Surface Q-Theory   Tollefson described a variant of normal surface theory for 3-manifolds,
called Q-theory, where only the quadrilateral coordinates are used. Suppose $M$
is a triangulated, compact, irreducible, boundary-irreducible 3-manifold. In
Q-theory, if $M$ contains an essential surface, then the projective solution
space has an essential surface at a vertex. One interesting situation not
covered by this theorem is when $M$ is boundary reducible, e.g. $M$ is an
unknot complement. We prove that in this case $M$ has an essential disc at a
vertex of the Q-projective solution space.

30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys