2022/04/05 by Edgar A. Bering, Christopher J. Leininger, Bering, Edgar A. +1
Computer Science · Mathematics · #57M50 05C25 20E36 20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2204.02204
openalex publication_date 2022/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A subcomplex X≤ C of a simplicial complex is strongly rigid if every locally injective, simplicial map X\toC 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.