Tohoku Mathematical Journal

Closed three-dimensional Alexandrov spaces with isometric circle actions

Jesús Núñez-Zimbrón

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Abstract

We obtain a topological and weakly equivariant classification of closed three-dimensional Alexandrov spaces with an effective, isometric circle action. This generalizes the topological and equivariant classifications of Raymond [26] and Orlik and Raymond [23] of closed three-dimensional manifolds admitting an effective circle action. As an application, we prove a version of the Borel conjecture for closed three-dimensional Alexandrov spaces with circle symmetry.

Article information

Source
Tohoku Math. J. (2), Volume 70, Number 2 (2018), 267-284.

Dates
First available in Project Euclid: 2 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1527904822

Digital Object Identifier
doi:10.2748/tmj/1527904822

Mathematical Reviews number (MathSciNet)
MR3810241

Zentralblatt MATH identifier
06929335

Subjects
Primary: 53C60: Finsler spaces and generalizations (areal metrics) [See also 58B20]
Secondary: 57M60: Group actions in low dimensions 57S25: Groups acting on specific manifolds

Keywords
3-manifold circle action Alexandrov space

Citation

Núñez-Zimbrón, Jesús. Closed three-dimensional Alexandrov spaces with isometric circle actions. Tohoku Math. J. (2) 70 (2018), no. 2, 267--284. doi:10.2748/tmj/1527904822. https://projecteuclid.org/euclid.tmj/1527904822


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