Leray Numbers of Tolerance Complexes

Abstract Let K be a simplicial complex on vertex set V . is called d - Leray if the homology groups of any induced subcomplex are trivial in dimensions and higher. collapsible it can reduced to void by sequentially removing simplex size at most that contained unique maximal face. Motivated results Eckhoff Montejano Oliveros “tolerant” versions Helly’s theorem, we define t tolerance , $${\mathcal {T}}_{t}(K)$$ T t ( K ) as whose simplices formed union We prove for there exists positive integer h ( ) such that, every -collapsible -tolerance {T}}_t(K)$$ )-Leray. As an application, present some new tolerant colorful Helly theorem.