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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The diffeotopy group of the twisted $ 2$-sphere bundle over the circle


Authors: M. Ho Kim and Frank Raymond
Journal: Trans. Amer. Math. Soc. 322 (1990), 159-168
MSC: Primary 57R50; Secondary 57N10
MathSciNet review: 991965
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Abstract: The diffeotopy group of the nontrivial $ 2$-sphere bundle over the circle is shown to be isomorphic to $ {\mathbb{Z}_2} \oplus {\mathbb{Z}_2}$. The first generator is induced by a reflection across the base circle, while a second generator comes from rotating the $ 2$-sphere fiber as one travels around the base circle. The technique employed also shows that homotopic diffeomorphisms are diffeotopic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0991965-6
PII: S 0002-9947(1990)0991965-6
Keywords: Diffeotopy, twisted $ {S^2}$-bundle over the circle, diffeomorphism, diffeotopy group, $ {S^1} \times {S^2}$
Article copyright: © Copyright 1990 American Mathematical Society