Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knots in collapsible and non-collapsible balls   We construct the first explicit example of a simplicial 3-ball B_{15,66} that
is not collapsible. It has only 15 vertices. We exhibit a second 3-ball
B_{12,38} with 12 vertices that is collapsible and evasive, but not shellable.
Finally, we present the first explicit triangulation of a 3-sphere S_{18, 125}
(with only 18 vertices) that is not locally constructible. All these examples
are based on knotted subcomplexes with only three edges; the knots are the
trefoil, the double trefoil, and the triple trefoil, respectively. The more
complicated the knot is, the more distant the triangulation is from being
polytopal, collapsible, etc. Further consequences of our work are:
  (1) Unshellable 3-spheres may have vertex-decomposable barycentric
subdivisions.
  (This shows the strictness of an implication proven by Billera and Provan.)
  (2) For d-balls, vertex-decomposable implies non-evasive implies collapsible,
and for d=3 all implications are strict.
  (This answers a question by Barmak.)
  (3) Locally constructible 3-balls may contain a double trefoil knot as a
3-edge subcomplex.
  (This improves a result of Benedetti and Ziegler.)
  (4) Rudin's ball is non-evasive.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas