Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher connectivity of the Morse complex   The Morse complex $\mathcal{M}(\Delta)$ of a finite simplicial complex
$\Delta$ is the complex of all gradient vector fields on $\Delta$. In this
paper we study higher connectivity properties of $\mathcal{M}(\Delta)$. For
example, we prove that $\mathcal{M}(\Delta)$ gets arbitrarily highly connected
as the maximum degree of a vertex of $\Delta$ goes to $\infty$, and for
$\Delta$ a graph additionally as the number of edges goes to $\infty$. We also
classify precisely when $\mathcal{M}(\Delta)$ is connected or simply connected.
Our main tool is Bestvina-Brady Morse theory, applied to a "generalized Morse
complex."

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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph