Factorization of differentiable maps with branch set dimension at most $n-3$
HTML articles powered by AMS MathViewer
- by P. T. Church
- Trans. Amer. Math. Soc. 115 (1965), 370-387
- DOI: https://doi.org/10.1090/S0002-9947-1965-0195101-3
- PDF | Request permission
References
- Richard F. Arens, A topology for spaces of transformations, Ann. of Math. (2) 47 (1946), 480–495. MR 17525, DOI 10.2307/1969087
- Edward G. Begle, The Vietoris mapping theorem for bicompact spaces, Ann. of Math. (2) 51 (1950), 534–543. MR 35015, DOI 10.2307/1969366
- Jean Cerf, Topologie de certains espaces de plongements, Bull. Soc. Math. France 89 (1961), 227–380 (French). MR 140120, DOI 10.24033/bsmf.1567
- P. T. Church, Differentiable open maps, Bull. Amer. Math. Soc. 68 (1962), 468–469. MR 149496, DOI 10.1090/S0002-9904-1962-10777-0
- 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, On points of Jacobian rank $k$, Trans. Amer. Math. Soc. 110 (1964), 413–423. MR 157390, DOI 10.1090/S0002-9947-1964-0157390-X
- Ralph H. Fox, Covering spaces with singularities, Algebraic geometry and topology. A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N.J., 1957, pp. 243–257. MR 0123298
- André Haefliger, Differentiable imbeddings, Bull. Amer. Math. Soc. 67 (1961), 109–112. MR 123337, DOI 10.1090/S0002-9904-1961-10522-3
- Sze-tsen Hu, Homotopy theory, Pure and Applied Mathematics, Vol. VIII, Academic Press, New York-London, 1959. MR 0106454
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493 J. Milnor, Differentiable manifolds which are homotopy spheres, Mimeographed, Princeton University, Princeton, N. J., 1958. —, Differential topology, Mimeographed, Princeton University, Princeton, N. J., 1958.
- John Milnor, On manifolds homeomorphic to the $7$-sphere, Ann. of Math. (2) 64 (1956), 399–405. MR 82103, DOI 10.2307/1969983
- Marston Morse, On elevating manifold differentiability, J. Indian Math. Soc. (N.S.) 24 (1960), 379–400 (1961). MR 141135
- James R. Munkres, Elementary differential topology, Annals of Mathematics Studies, No. 54, Princeton University Press, Princeton, N.J., 1963. Lectures given at Massachusetts Institute of Technology, Fall, 1961. MR 0163320, DOI 10.1515/9781400882656
- Richard S. Palais, Extending diffeomorphisms, Proc. Amer. Math. Soc. 11 (1960), 274–277. MR 117741, DOI 10.1090/S0002-9939-1960-0117741-0
- Richard S. Palais, Local triviality of the restriction map for embeddings, Comment. Math. Helv. 34 (1960), 305–312. MR 123338, DOI 10.1007/BF02565942
- Richard S. Palais, Natural operations on differential forms, Trans. Amer. Math. Soc. 92 (1959), 125–141. MR 116352, DOI 10.1090/S0002-9947-1959-0116352-7
- Arthur Sard, Hausdorff measure of critical images on Banach manifolds, Amer. J. Math. 87 (1965), 158–174. MR 173748, DOI 10.2307/2373229
- Arthur Sard, The measure of the critical values of differentiable maps, Bull. Amer. Math. Soc. 48 (1942), 883–890. MR 7523, DOI 10.1090/S0002-9904-1942-07811-6
- Shlomo Sternberg and Richard G. Swan, On maps with nonnegative Jacobian, Michigan Math. J. 6 (1959), 339–342. MR 111051
- René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 61823, DOI 10.1007/BF02566923
- A. W. Tucker, Branched and folded coverings, Bull. Amer. Math. Soc. 42 (1936), no. 12, 859–862. MR 1563453, DOI 10.1090/S0002-9904-1936-06446-3
- Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR 0007095, DOI 10.1090/coll/028
- R. L. Wilder, Monotone mappings of manifolds. II, Michigan Math. J. 5 (1958), 19–23. MR 97798, DOI 10.1307/mmj/1028998007 —, Topology of manifolds, Amer. Math. Soc. Colloq. Publ. Vol. 32, Amer. Math. Soc., Providence, R. I., 1949.
Bibliographic Information
- © Copyright 1965 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 115 (1965), 370-387
- MSC: Primary 57.20
- DOI: https://doi.org/10.1090/S0002-9947-1965-0195101-3
- MathSciNet review: 0195101