Full Subcomplexes of CAT(0) Simplicial Complexes
Rena M.H. Levitt
TL;DR
This paper proves that full subcomplexes of CAT(0) simplicial 3-complexes maintain non-positive curvature, but this property does not extend to higher dimensions, as shown by counterexamples.
Contribution
It establishes the inheritance of non-positive curvature for full subcomplexes in 3-dimensional CAT(0) simplicial complexes and highlights limitations in higher dimensions.
Findings
Full subcomplexes of CAT(0) 3-complexes are also CAT(0).
Counterexamples show the property fails in higher dimensions.
The result clarifies curvature inheritance in low-dimensional complexes.
Abstract
In this article, I prove that full subcomplexes of CAT(0) simplicial 3-complexes inherit the non positive curvature condition, and describe a family of counterexamples that prove this result can not be extended to higher dimensions.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis