Papers › Betti splitting from a topological point of view
Betti splitting from a topological point of view
Davide Bolognini, Ulderico Fugacci
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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 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 Δ to the topological properties of Δ. 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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections