- Autor
- Bolognini, Davide
- Fugacci, Ulderico
- TitelBetti splitting from a topological point of view
- Datei
- Persistent Identifier
- Erschienen inJournal of Algebra and its Applications
- Erscheinungsjahr2018
- LicenceCC-BY
- Download Statistik863
- Peer ReviewJa
- Abstract 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 \(J \cap K\). In this paper, we introduce this condition for simplicial complexes, and, by using Alexander duality, we prove that it is equivalent to a recursive splitting conditions on links of some vertices. The adopted point of view enables for relating the existence of a Betti splitting for a simplicial complex \(\Delta\) to the topological properties of \(\Delta\). Among other results, we prove that orientability for a manifold without boundary is equivalent to admit a Betti splitting induced by the removal of a single facet. Taking advantage of this topological approach, we provide the first example in literature admitting Betti splitting but with characteristic-dependent resolution. Moreover, we introduce the notion of splitting probability, useful to deal with results concerning existence of Betti splitting.
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