Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thirty-five years and counting   It has been 35 years since Stanley proved that f-vectors of boundaries of
simplicial polytopes satisfy McMullen's conjectured g-conditions. Since then
one of the outstanding questions in the realm of face enumeration is whether or
not Stanley's proof could be extended to larger classes of spheres. Here we
hope to give an overview of various attempts to accomplish this and why we feel
this is so important. In particular, we will see a strong connection to
f-vectors of manifolds and pseudomanifolds. Along the way we have included
several previously unpublished results involving how the g-conjecture relates
to bistellar moves and small g_2, the topology and combinatorics of stacked
manifolds introduced independently by Bagchi and Datta, and Murai and Nevo, and
counterexamples to over optimistic generalizations of the g-theorem.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph