Betti splitting from a topological point of view

Davide Bolognini*, Ulderico Fugacci

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A Betti splitting I = J + K of a monomial ideal I ensures the recovery of the graded Betti numbers of I starting from those of J,K and J K. In this paper, we introduce an analogous notion for simplicial complexes, using Alexander duality, proving that it is equivalent to a recursive splitting condition on links of some vertices. We provide results ensuring the existence of a Betti splitting for a simplicial complex , relating it to topological properties of . Among other things, we prove that orientability for a manifold without boundary is equivalent to the admission of a Betti splitting induced by the removal of a single facet. Taking advantage of our topological approach, we provide the first example of a monomial ideal which admits Betti splittings in all characteristics but with characteristic-dependent resolution. Moreover, we introduce new numerical descriptors for simplicial complexes and topological spaces, useful to deal with questions concerning the existence of Betti splitting.

Original languageEnglish
Article number2050116
JournalJournal of Algebra and its Applications
Issue number6
Publication statusPublished - 1 Jun 2020


  • Graded Betti numbers
  • simplicial complexes
  • triangulated manifolds

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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