Expansive homeomorphisms on compact manifolds
Author:
Thomas O’Brien
Journal:
Proc. Amer. Math. Soc. 24 (1970), 767-771
MSC:
Primary 54.82
DOI:
https://doi.org/10.1090/S0002-9939-1970-0253308-8
MathSciNet review:
0253308
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper theorems are proved which provide for lifting and projecting expansive homeomorphisms through pseudo-covering mappings so that the lift or projection is also an expansive homeomorphism. Using these techniques it is shown that the compact orientable surface of genus $2$ admits an expansive homeomorphism.
- B. F. Bryant, Expansive Self-Homeomorphisms of a Compact Metric Space, Amer. Math. Monthly 69 (1962), no. 5, 386–391. MR 1531676, DOI https://doi.org/10.2307/2312129
- Philip T. Church and Erik Hemmingsen, Light open maps on $n$-manifolds, Duke Math. J. 27 (1960), 527–536. MR 116315
- Ralph H. Fox, Covering spaces with singularities, A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N.J., 1957, pp. 243–257. MR 0123298
- E. Hemmingsen and W. L. Reddy, Lifting and projecting expansive homeomorphisms, Math. Systems Theory 2 (1968), 7–15. MR 222855, DOI https://doi.org/10.1007/BF01691342
- William Reddy, The existence of expansive homeomorphisms on manifolds, Duke Math. J. 32 (1965), 627–632. MR 187226
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Additional Information
Keywords:
Expansive homeomorphism,
pseudo-covering map,
lifting,
fundamental group
Article copyright:
© Copyright 1970
American Mathematical Society