Nonpositive Towers in Bing's Neighbourhood
Max Chemtov, Daniel T. Wise
TL;DR
This paper investigates the properties of 2-dimensional spines in 3-manifolds, showing that certain aspherical manifolds have nonpositive towers, while collapsed spines in 3-balls contain immersed spheres.
Contribution
It establishes the nonpositive towers property for 2-dimensional spines of aspherical 3-manifolds and highlights the difference in collapsed spines of 3-balls.
Findings
Aspherical 3-manifolds' spines have nonpositive towers
Collapsed spines in 3-balls contain immersed spheres
Distinction between properties of different spines
Abstract
Every 2-dimensional spine of an aspherical 3-manifold has the nonpositive towers property, but every collapsed 2-dimensional spine of a 3-ball containing a 2-cell has an immersed sphere.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Geometric and Algebraic Topology · Mathematics and Applications