Abstract
Various standard texts on differential topology maintain that the level-preserving map defined by the track of an isotopy of embeddings is itself an embedding. This note describes a simple counterexample to this assertion.
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References
Th. Bröcker and K. Jänich, Einführung in die Differentialtopologie, Heidelberger Taschenbücher, 143, Springer-Verlag, Berlin, 1973.
M. W. Hirsch, Differential Topology, Grad. Texts in Math., 33, Springer-Verlag, Berlin 1976.
A. A. Kosinski, Differential Manifolds, Pure Appl. Math., 138, Academic Press, Boston, MA, 1993.
A. Mukherjee, Differential Topology, 2nd edition, Birkhäuser Verlag, Basel, 2015.
A. R. Shastri, Elements of Differential Topology, CRC Press, Boca Raton, FL, 2011.
C. T. C. Wall, Differential Topology, Cambridge Stud. Adv. Math., 156, Cambridge University Press, Cambridge, 2016.
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Geiges, H. Isotopies vis-à-vis level-preserving embeddings. Arch. Math. 110, 197–200 (2018). https://doi.org/10.1007/s00013-017-1109-1
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DOI: https://doi.org/10.1007/s00013-017-1109-1