For fixed simplicial complexes, the fibers of multiparameter persistent homology are trivial polyhedral bundles over each stratum, with dimension bounded by multigraded Betti numbers.
‘Morse inequalities for the Koszul complex of multi-persistence’
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The fiber of multiparameter persistent homology for simplicial complexes
For fixed simplicial complexes, the fibers of multiparameter persistent homology are trivial polyhedral bundles over each stratum, with dimension bounded by multigraded Betti numbers.