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finite topological spaces

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Morse theory of Bestvina–Brady type for posets and matchings
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Elías Gabriel Minian
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 154 / Issue 1 / February 2024

Published online by Cambridge University Press:

09 February 2023, pp. 209-220

Print publication:

February 2024
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We introduce a Morse theory for posets of Bestvina–Brady type combining matchings and height functions. This theory generalizes Forman's discrete Morse theory for regular CW-complexes and extends previous results on Morse theory for $h$-regular posets to all finite posets. We also develop a relative version of Morse theory which allows us to compare the topology of a poset with that of a given subposet.