Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on Lefschetz spheres and their relatives   Inspired by the works of Adiprasito, Babson, Nevo, and Murai on the
$g$-conjecture, we consider different classes of PL-spheres and the relations
between them. We focus on a certain class of spheres that is in the
intersection of vertex-decomposable spheres (a concept due to Provan and
Billera) and strongly edge-decomposable spheres (a concept due to Eran Nevo).
The spheres in this class are exactly those vertex-decomposable ones for which
Adiprasito's recent proof method works.

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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
3
The categories of this paper are: physics