Defines bigraded path homology from the MPSS connecting magnitude and path homology, proves it and all MPSS pages satisfy excision and Kunneth theorems, establishes Mayer-Vietoris for magnitude and bigraded versions, builds a cofibration category with bigraded isomorphisms as weak equivalences, and
Ivanov,Nested homotopy models of finite metric spaces and their spectral homology, (2024), arxiv:2312.11878
3 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 3representative citing papers
Defines r-quasi-isomorphisms and r-cofibrations on generalized metric spaces so that each page of the magnitude-path spectral sequence satisfies metric Eilenberg-Steenrod axioms and supports Brown category structures for homotopy colimits, restricting to directed graphs at r=1.
Defines rank-filtered subcomplexes of order complexes of graded posets and proves their homology matches manifold homology except in top degree, plus shellability and wedge-of-spheres homotopy types for shellable and geometric semilattice cases.
citing papers explorer
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Bigraded path homology and the magnitude-path spectral sequence
Defines bigraded path homology from the MPSS connecting magnitude and path homology, proves it and all MPSS pages satisfy excision and Kunneth theorems, establishes Mayer-Vietoris for magnitude and bigraded versions, builds a cofibration category with bigraded isomorphisms as weak equivalences, and
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Homotopy theories via the magnitude-path spectral sequence
Defines r-quasi-isomorphisms and r-cofibrations on generalized metric spaces so that each page of the magnitude-path spectral sequence satisfies metric Eilenberg-Steenrod axioms and supports Brown category structures for homotopy colimits, restricting to directed graphs at r=1.
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Filtered order complexes and magnitude homology of finite graded posets
Defines rank-filtered subcomplexes of order complexes of graded posets and proves their homology matches manifold homology except in top degree, plus shellability and wedge-of-spheres homotopy types for shellable and geometric semilattice cases.