The fundamental group of random $2$-complexes
نویسندگان
چکیده
منابع مشابه
The Fundamental Group of Random 2-complexes
In this article we find the threshold for simple connectivity of the random 2dimensional simplicial complexes Y (n, p) introduced by Linial and Meshulam [10] to be roughly p = n−1/2. One motivation for this is continuing the thread of probabilistic topology initiated by Linial and Meshulam [10], and even earlier by Erdős and Rényi [3]. (Other recent work concerning the topology of random simpli...
متن کاملFundamental Groups of Random Clique Complexes
Clique complexes of Erdős-Rényi random graphs with edge probability between n− 1 3 and n− 1 2 are shown to be aas not simply connected. This entails showing that a connected two dimensional simplicial complex for which every subcomplex has fewer than three times as many edges as vertices must have the homotopy type of a wedge of circles, two spheres and real projective planes. Note that n− 1 3 ...
متن کاملAlgebraic fundamental group and simplicial complexes
In this paper we prove that the fundamental group of a simplicial complex is isomorphic to the algebraic fundamental group of its incidence algebra, and we derive some applications. AMS classification : 16E40 ; 16G20 ; 06A11 ; 55Q05 Let k be a field and A be a basic and split finite dimensional k-algebra, which means that A/r = k× k× . . .× k where r is the radical of A. There exists a unique q...
متن کاملThe Fundamental Group of Balanced Simplicial Complexes and Posets
We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.
متن کاملThe asphericity of random 2-dimensional complexes
We study random 2-dimensional complexes in the Linial Meshulam model and prove that for the probability parameter satisfying p ≪ n a random 2-complex Y contains several pairwise disjoint tetrahedra such that the 2-complex Z obtained by removing any face from each of these tetrahedra is aspherical. Moreover, we prove that the obtained complex Z satisfies the Whitehead conjecture, i.e. any subcom...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2011
ISSN: 0894-0347
DOI: 10.1090/s0894-0347-2010-00677-7