Tohoku Mathematical Journal
2018

June
SECOND SERIES VOL. 70, NO. 2

Tohoku Math. J.
70 (2018), 267-284

Title CLOSED THREE-DIMENSIONAL ALEXANDROV SPACES WITH ISOMETRIC CIRCLE ACTIONS

Author Jesús Núñez-Zimbrón

(Received December 5, 2013, revised March 16, 2016)
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.

Mathematics Subject Classification. Primary 53C60; Secondary 57M60, 57S25.

Key words and phrases. 3-manifold, circle action, Alexandrov space.

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