Positively expansive maps and growth of fundamental groups

Hiraide, K.

doi:10.1090/S0002-9939-1988-0964877-8

Positively expansive maps and growth of fundamental groups
HTML articles powered by AMS MathViewer

by K. Hiraide

Proc. Amer. Math. Soc. 104 (1988), 934-941

DOI: https://doi.org/10.1090/S0002-9939-1988-0964877-8

PDF | Request permission

Abstract:

In this note we will show that a positively expansive map of an arbitrary closed topological manifold is topologically conjugate to an expanding infra-nil-endomorphism.

References

N. Aoki and K. Hiraide, The linearization of positively expansive maps of tori, The theory of dynamical systems and its applications to nonlinear problems (Kyoto, 1984) World Sci. Publishing, Singapore, 1984, pp. 27–31. MR 797595
Ethan M. Coven and William L. Reddy, Positively expansive maps of compact manifolds, Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979) Lecture Notes in Math., vol. 819, Springer, Berlin, 1980, pp. 96–110. MR 591178
P. F. Duvall Jr. and L. S. Husch, Analysis on topological manifolds, Fund. Math. 77 (1972), no. 1, 75–90. MR 367952, DOI 10.4064/fm-77-1-75-90
John Franks, Anosov diffeomorphisms, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 61–93. MR 0271990
Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. MR 623534
R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742–749. MR 242166, DOI 10.1090/S0002-9904-1969-12271-8
J. Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968), 1–7. MR 232311
Michael Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175–199. MR 240824, DOI 10.2307/2373276
Michael Shub, Expanding maps, Global Analysis (Proc. Sympos. Pure Math., Vols. XIV, XV, XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 273–276. MR 0266251
Joseph A. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geometry 2 (1968), 421–446. MR 248688