Annals of Global Analysis and Geometry

, Volume 41, Issue 1, pp 47–59

Orbifold homeomorphism finiteness based on geometric constraints

Original Paper

Abstract

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold homeomorphism types. This is a generalization to the orbifold category of a similar result for manifolds proven by Grove, Petersen, and Wu. It follows that any Laplace isospectral collection of orbifolds with sectional curvature uniformly bounded below and having only isolated singular points also contains only finitely many orbifold homeomorphism types. The main steps of the argument are to show that any sequence from the collection has subsequence that converges to an orbifold, and then to show that the homeomorphism between the underlying spaces of the limit orbifold and an orbifold from the subsequence that is guaranteed by Perelman’s stability theorem must preserve orbifold structure.

Keywords

Orbifold Global Riemannian geometry Alexandrov space Spectral geometry 

Mathematics Subject Classification (2000)

Primary 53C23 Secondary 53C20 58J53 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsMiddlebury CollegeMiddleburyUSA

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