Topological finiteness theorems for manifolds in Gromov-Hausdorff space

1994/04/01 by Steven C. Ferry · 2 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · doi:10.1215/s0012-7094-94-07404-8

Abstract

We give general conditions under which precompact sets of topological manifolds in Gromov-Hausdorff space contain finitely many homeomorphism types. The main result says that this is true if the manifolds in the set have a common contractibility function. We also show that there are at most finitely many closed n-manifolds, n 6= 3, with a common cell-like image.

Citations

• Approximating Homotopy Equivalences by Homeomorphisms
• Curvature, tangentiality, and controlled topology

Cited by

• Cell-Like Maps and Surgery
• Notes on metrics, measures, and dimensions

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