Publication Date
4-15-2024
Document Type
Article
Publication Title
Topology and its Applications
Volume
347
DOI
10.1016/j.topol.2024.108862
Abstract
A subcomplex X≤C of a simplicial complex is strongly rigid if every locally injective, simplicial map X→C is the restriction of a unique automorphism of C. Aramayona and the second author proved that the curve complex of an orientable surface can be exhausted by finite strongly rigid sets. The Hatcher sphere complex is an analog of the curve complex for isotopy classes of essential spheres in a connect sum of n copies of S1×S2. We show that there is an exhaustion of the sphere complex by finite strongly rigid sets for all n≥3 and that when n=2 the sphere complex does not have finite rigid sets.
Funding Number
DMS-2106419
Funding Sponsor
National Science Foundation
Keywords
Outer automorphism group, Rigidity, Sphere complex
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Department
Mathematics and Statistics
Recommended Citation
Edgar A. Bering and Christopher J. Leininger. "Finite rigid sets in sphere complexes" Topology and its Applications (2024). https://doi.org/10.1016/j.topol.2024.108862
