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

Kim, M. Ho; Raymond, Frank

doi:10.1090/S0002-9947-1990-0991965-6

The diffeotopy group of the twisted $2$-sphere bundle over the circle
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by M. Ho Kim and Frank Raymond PDF

Trans. Amer. Math. Soc. 322 (1990), 159-168 Request permission

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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