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...
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Published in | Discrete & computational geometry Vol. 67; no. 4; pp. 1229 - 1244 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.06.2022
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0179-5376 1432-0444 |
DOI: | 10.1007/s00454-021-00352-x |