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A characterisation of S³ among homology spheres
Michel Boileau, Luisa Paoluzzi and Bruno Zimmermann
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Geometry & Topology Monographs 14
(2008) 83–103
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Abstract
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We prove that an integral homology 3–sphere is S3 if
and only if it admits four periodic diffeomorphisms of odd prime
orders whose space of orbits is S3. As an application we
show that an irreducible integral homology sphere which is not
S3 is the cyclic branched cover of odd prime order of at
most four knots in S3. A result on the structure of finite
groups of odd order acting on integral homology spheres is also
obtained.
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To the memory of Heiner
Zieschang
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Keywords
homology sphere, geometric structure,
3-manifold, cyclic branched covers, finite group action
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Mathematical Subject Classification
Primary: 57M40
Secondary: 57M12, 57M50, 57M60, 57S17
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Publication
Received: 8 June 2006
Accepted: 11 April 2007
Published: 29 April 2008
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