## View abstract

### Session S27 - Categories and Topology

Friday, July 16, 12:00 ~ 12:30 UTC-3

## Connectivity of random simplicial complexes

### Jonathan Barmak

#### IMAS/Universidad de Buenos Aires, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakb622202f133578dbb164098f54575313').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyb622202f133578dbb164098f54575313 = 'jb&#97;rm&#97;k' + '&#64;'; addyb622202f133578dbb164098f54575313 = addyb622202f133578dbb164098f54575313 + 'dm' + '&#46;' + '&#117;b&#97;' + '&#46;' + '&#97;r'; var addy_textb622202f133578dbb164098f54575313 = 'jb&#97;rm&#97;k' + '&#64;' + 'dm' + '&#46;' + '&#117;b&#97;' + '&#46;' + '&#97;r';document.getElementById('cloakb622202f133578dbb164098f54575313').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyb622202f133578dbb164098f54575313 + '\'>'+addy_textb622202f133578dbb164098f54575313+'<\/a>';

A simplicial complex is $r$-conic if every subcomplex of at most $r$ vertices is contained in a cone. We prove that for any $d\ge 0$ there exists $r$ such that $r$-conicity implies $d$-connectivity of the polyhedron. On the other hand, for a fixed $r$, the probability of a random simplicial complex being $r$-conic tends to $1$ as the number of vertices tends to $\infty$. Thus, random complexes are $d$-connected with high probability.