Monomial ideals with up to four generators always admit a polyhedral Morse resolution, but there is a six-generator ideal for which no Morse matching yields a polyhedral Morse complex and no minimal polyhedral resolution exists at all.
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When are Morse resolutions polyhedral?
Monomial ideals with up to four generators always admit a polyhedral Morse resolution, but there is a six-generator ideal for which no Morse matching yields a polyhedral Morse complex and no minimal polyhedral resolution exists at all.