Free involutions on S1 × Sn

Topological free involutions on S 1 × S n are classified up to conjugation. We prove that this is the same as classifying quotient manifolds up to homeomorphism. There are exactly four possible homotopy types of such quotients, and surgery theory is used to classify all manifolds within each homoto...

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Veröffentlicht in:	Mathematische annalen 2011, Vol.351 (2), p.281-303
Hauptverfasser:	Jahren, Bjørn, Kwasik, Sławomir
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
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Zusammenfassung:	Topological free involutions on S 1 × S n are classified up to conjugation. We prove that this is the same as classifying quotient manifolds up to homeomorphism. There are exactly four possible homotopy types of such quotients, and surgery theory is used to classify all manifolds within each homotopy type.
ISSN:	0025-5831 1432-1807
DOI:	10.1007/s00208-010-0599-y