Topology and Geometry of Random 2-Dimensional Hypertrees

A hypertree, or Q -acyclic complex, is a higher-dimensional analogue of a tree. We study random 2-dimensional hypertrees according to the determinantal measure suggested by Lyons. We are especially interested in their topological and geometric properties. We show that with high probability, a random...

Full description

Saved in:
Bibliographic Details
Published inDiscrete & computational geometry Vol. 67; no. 4; pp. 1229 - 1244
Main Authors Kahle, Matthew, Newman, Andrew
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2022
Springer Nature B.V
Subjects
Combinatorics
Computational Mathematics and Numerical Analysis
Geometry
Mathematics
Mathematics and Statistics
Probability distribution
Topology
Trees
Hypertrees
55U10
Random simplicial complexes
Hyperbolic groups
20F67
60B99
Online AccessGet full text

Cover

More Information
Summary:A hypertree, or Q -acyclic complex, is a higher-dimensional analogue of a tree. We study random 2-dimensional hypertrees according to the determinantal measure suggested by Lyons. We are especially interested in their topological and geometric properties. We show that with high probability, a random 2-dimensional hypertree T is aspherical, i.e., that it has a contractible universal cover. We also show that with high probability the fundamental group π 1 ( T ) is hyperbolic and has cohomological dimension 2.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-021-00352-x