Collapsing three-manifolds under a lower curvature bound

Takashi Shioya; Takao Yamaguchi

doi:10.4310/jdg/1090347524

Collapsing three-manifolds under a lower curvature bound

Takashi Shioya, Takao Yamaguchi

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

The purpose of this paper is to completely characterize the topology of threedimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension.

Original language	English
Pages (from-to)	1-66
Number of pages	66
Journal	Journal of Differential Geometry
Volume	56
Issue number	1
DOIs	https://doi.org/10.4310/jdg/1090347524
Publication status	Published - 2000

Keywords

Alexandrov spaces
Seifert fibred spaces
The Gromov-Hausdorff convergence
Topology of three-manifolds

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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title = "Collapsing three-manifolds under a lower curvature bound",

abstract = "The purpose of this paper is to completely characterize the topology of threedimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension.",

keywords = "Alexandrov spaces, Seifert fibred spaces, The Gromov-Hausdorff convergence, Topology of three-manifolds",

author = "Takashi Shioya and Takao Yamaguchi",

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KW - The Gromov-Hausdorff convergence

KW - Topology of three-manifolds

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