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Surgery description of orientation-preserving periodic maps on compact orientable 3-manifolds
Sakuma, Makoto
2001
Abstract
We show that every orientation-preserving periodic diffeomorphism
f on a closed orientable 3-manifold M has a \textquotedblleft{}surgery
description\textquotedblright{}, that is, there is a framed link $\mathcal{L}\;\textrm{in}\; S^{3}$
which is invariant by a standard rotation $\varphi$ around a trivial
knot, such that M is obtained by surgery on $\varphi$ and that f
is conjugate to the periodic diff{}eomorphism induced by $\varphi$.
We will illustrate this result, by visualizing isometries of the complements
of 2-component hyperbolic links with $\leq$ 9 crossings which do
not extend to periodic maps of $S^{3}$.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 suppl. 1 (2001)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Makoto Sakuma, "Surgery description of orientation-preserving periodic maps on compact orientable 3-manifolds", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.1, pp. 375–396.
Languages
en
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