Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of normal 3-pseudomanifolds with at most two
  singularities   Characterizing face-number related invariants of a given class of simplicial
complexes has been a central topic in combinatorial topology. In this regard,
one of the most well-known invariants is $g_2$. Kalai's relative lower bound
[10] for $g_2$ says that if $K$ is a normal $d$-pseudomanifold with $d \geq 3,$
then $g_2(K) \geq g_2(lk (v))$ for any vertex $v$ of $K.$ In [7], two
combinatorial tools - `vertex folding' and `edge folding' were defined. Let $K$
be a normal $3$-pseudomanifold with at most two singularities (in case of two
singularities, we take one singularity as $\mathbb{RP}^2$). Let $t$ be a vertex
of $K$ with $g_2(lk (t)) \geq g_2(lk (v))$ for any other vertex $v$. We prove
that if $g_2{(K)} \leq g_2(lk (t)) + 9$ then $K$ is obtained from some boundary
complex of $4$-simplices by a sequence of operations connected sum, bistellar
$1$-move, edge contraction, edge expansion, vertex folding and edge folding.
Further, we prove that the upper bound is sharp for such combinatorial normal
$3$-pseudomanifolds.

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The categories of this paper are: hep-ph
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The categories of this paper are: cs
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th