The geometry of immersions. I

The geometry of immersions. I
HTML articles powered by AMS MathViewer

Trans. Amer. Math. Soc. 120 (1965), 185-224

DOI: https://doi.org/10.1090/S0002-9947-1965-0185602-6

PDF | Request permission

References

Ralph Abraham, Transversality in manifolds of mappings, Bull. Amer. Math. Soc. 69 (1963), 470–474. MR 149495, DOI 10.1090/S0002-9904-1963-10969-6
W. Ambrose, R. S. Palais, and I. M. Singer, Sprays, An. Acad. Brasil. Ci. 32 (1960), 163–178. MR 126234
M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957), 181–207. MR 86359, DOI 10.1090/S0002-9947-1957-0086359-5

Singularities of smooth maps

Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, N.J., 1952. MR 0050886
Edgar Feldman, The geometry of immersions. I, Bull. Amer. Math. Soc. 69 (1963), 693–698. MR 151986, DOI 10.1090/S0002-9904-1963-10988-X
Roger Godement, Topologie algébrique et théorie des faisceaux, Publ. Inst. Math. Univ. Strasbourg. No. 13, Hermann, Paris, 1958 (French). MR 0102797

Differential topology

John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
Shoshichi Kobayashi, Canonical forms on frame bundles of higher order contact, Proc. Sympos. Pure Math., Vol. III, American Mathematical Society, Providence, R.I., 1961, pp. 186–193. MR 0126810
J.-L. Koszul, Lectures on fibre bundles and differential geometry, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 20, Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1986. With notes by S. Ramanan; Reprint of the 1965 edition. MR 901943, DOI 10.1007/978-3-662-02503-1

Singularities of differentiable mappings

Calcul tensoriel et connexions d’ordre superieur

Characteristic classes

Differential topology

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
William Francis Pohl, Differential geometry of higher order, Topology 1 (1962), 169–211. MR 154293, DOI 10.1016/0040-9383(62)90103-9

Connexions in differential geometry of higher order

Arthur Sard, Images of critical sets, Ann. of Math. (2) 68 (1958), 247–259. MR 100063, DOI 10.2307/1970246
Jean-Pierre Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197–278 (French). MR 68874, DOI 10.2307/1969915
Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR 0039258
Dirk J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley Press, Inc., Cambridge, Mass., 1950. MR 0036551
Emery Thomas, On tensor products of $n$-plane bundles, Arch. Math. 10 (1959), 174–179. MR 107234, DOI 10.1007/BF01240783
Hassler Whitney, Differentiable manifolds, Ann. of Math. (2) 37 (1936), no. 3, 645–680. MR 1503303, DOI 10.2307/1968482
Hassler Whitney, On singularities of mappings of euclidean spaces. I. Mappings of the plane into the plane, Ann. of Math. (2) 62 (1955), 374–410. MR 73980, DOI 10.2307/1970070
Hassler Whitney, Geometric integration theory, Princeton University Press, Princeton, N. J., 1957. MR 0087148
Hassler Whitney, Elementary structure of real algebraic varieties, Ann. of Math. (2) 66 (1957), 545–556. MR 95844, DOI 10.2307/1969908
Hassler Whitney, On regular closed curves in the plane, Compositio Math. 4 (1937), 276–284. MR 1556973
Hassler Whitney, The singularities of a smooth $n$-manifold in $(2n-1)$-space, Ann. of Math. (2) 45 (1944), 247–293. MR 10275, DOI 10.2307/1969266