Monotone real analytic maps which are not homeomorphisms

Hsu, A. C.; Timourian, J. G.

doi:10.1090/S0002-9939-1975-0370623-2

Monotone real analytic maps which are not homeomorphisms
HTML articles powered by AMS MathViewer

by A. C. Hsu and J. G. Timourian

Proc. Amer. Math. Soc. 51 (1975), 231-236

DOI: https://doi.org/10.1090/S0002-9939-1975-0370623-2

PDF | Request permission

Abstract:

Monotone, proper, real analytic, onto maps which have nonempty branch sets are exhibited. The smash product maps are shown to belong to this class of maps. Maps with branch set a submanifold and with discrete branch set images are classified (locally).

References

William Browder, Higher torsion in $H$-spaces, Trans. Amer. Math. Soc. 108 (1963), 353–375. MR 155326, DOI 10.1090/S0002-9947-1963-0155326-8
P. T. Church, Differentiable monotone mappings and open mappings, Proc. First Conf. on Monotone Mappings and Open Mappings (SUNY at Binghamton, Binghamton, N.Y., 1970) State Univ. of New York at Binghamton, Binghamton, N.Y., 1971, pp. 145–183. MR 0281219
P. T. Church, Differentiable open maps on manifolds, Trans. Amer. Math. Soc. 109 (1963), 87–100. MR 154296, DOI 10.1090/S0002-9947-1963-0154296-6
P. T. Church and W. D. Nathan, Real analytic maps on manifolds, J. Math. Mech. 19 (1969/1970), 19–36. MR 0243539, DOI 10.1512/iumj.1970.19.19003
J. G. Timourian, Fiber bundles with discrete singular set, J. Math. Mech. 18 (1968/1969), 61–70. MR 0235571, DOI 10.1512/iumj.1969.18.18007
Andrew Wallace, Local cone structures on varieties, Indiana Univ. Math. J. 24 (1974/75), 131–141. MR 352087, DOI 10.1512/iumj.1974.24.24010