Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity and the Lower Bound Theorem for Doubly Cohen-Macaulay Complexes   We prove that for $d\geq 3$, the 1-skeleton of any $(d-1)$-dimensional doubly
Cohen Macaulay (abbreviated 2-CM) complex is generically $d$-rigid. This
implies the following two corollaries (by Kalai and Lee respectively):
Barnette's lower bound inequalities for boundary complexes of simplicial
polytopes hold for every 2-CM complex (of dimension $\geq 2$). Moreover, the
initial part $(g_0,g_1,g_2)$ of the $g$-vector of a 2-CM complex (of dimension
$\geq 3$) is an $M$-sequence. It was conjectured by Bj\"{o}rner and Swartz that
the entire $g$-vector of a 2-CM complex is an $M$-sequence.

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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc