Extensions of codimension one immersions
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- by Christian Pappas
- Trans. Amer. Math. Soc. 348 (1996), 3065-3083
- DOI: https://doi.org/10.1090/S0002-9947-96-01572-3
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Abstract:
We give a method for constructing all of the extensions of an immersion, and determine the CW structure and diffeomorphism type of each.References
- George K. Francis, Extensions to the disk of properly nested plane immersions of the circle, Michigan Math. J. 17 (1970), 377–383. MR 284985
- Morris W. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242–276. MR 119214, DOI 10.1090/S0002-9947-1959-0119214-4
- Morris W. Hirsch, Differential topology, Graduate Texts in Mathematics, No. 33, Springer-Verlag, New York-Heidelberg, 1976. MR 0448362, DOI 10.1007/978-1-4684-9449-5
- John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554, DOI 10.1515/9781400881826
- J. Milnor, Morse theory, Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. Based on lecture notes by M. Spivak and R. Wells. MR 0163331, DOI 10.1515/9781400881802
- C. Pappas, The full two dimensional homotopy group, $\rho _2(X)$, preprint.
- —, Extensions of immersions into Euclidean spaces, Thesis, Univ. of California, Berkeley, 1994.
- V. Poénaru, Extension des immersions en codimension one (d’après S. Blank), Séminaire Bourbaki, 1968, no. 342.
- Stephen Smale, On gradient dynamical systems, Ann. of Math. (2) 74 (1961), 199–206. MR 133139, DOI 10.2307/1970311
- Stephen Smale, The classification of immersions of spheres in Euclidean spaces, Ann. of Math. (2) 69 (1959), 327–344. MR 105117, DOI 10.2307/1970186
- J. H. C. Whitehead, The immersion of an open $3$-manifold in euclidean $3$-space, Proc. London Math. Soc. (3) 11 (1961), 81–90. MR 124916, DOI 10.1112/plms/s3-11.1.81
Bibliographic Information
- Christian Pappas
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- Email: pappas@math.berkeley.edu
- Received by editor(s): January 1, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 3065-3083
- MSC (1991): Primary 57R42
- DOI: https://doi.org/10.1090/S0002-9947-96-01572-3
- MathSciNet review: 1344210