Conic simplicial complexes

BARMAK, JONATHAN ARIEL

Londres

Seminario; Institute Applied Data Science, Queen Mary, London University; 2021

Institute Applied Data Science, Queen Mary, London University

A simplicial complex K is r-conic if every subcomplex of at most r vertices is contained in a cone. We will see that for every n there exists r such that r-conicity implies n-connectivity. This proves a conjecture implicitly stated by Even-Zohar, Farber and Mead involving the notion of an ample complex. Our results together imply that the probability of a random complex being n-connected tends to 1 when the number of vertices tends to infinity.