2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169392We show that the algebraic intersection number of Scott and Swarup for splittings of free groups coincides with the geometric intersection number for the sphere complex of the connected sum of copies of $S^2\times S^1$.7 pagesGeometric TopologyGroup Theory57M05 (Primary) 57M07, 20E06 (Secondary)text