Some new embeddings and nonimmersions of real projective spaces
HTML articles powered by AMS MathViewer
- by Donald M. Davis and Vitaly Zelov PDF
- Proc. Amer. Math. Soc. 128 (2000), 3731-3740 Request permission
Abstract:
We obtain new families of embeddings and nonimmersions of real projective spaces in Euclidean space. The method involves obstruction theory, and includes several new insights.References
- L. Astey and D. M. Davis, Nonimmersions of real projective spaces implied by $BP$, Bol Soc Mat Mex 24 (1979) 49-55.
- Donald M. Davis, Some new immersions and nonimmersions of real projective spaces, Proceedings of the Northwestern Homotopy Theory Conference (Evanston, Ill., 1982) Contemp. Math., vol. 19, Amer. Math. Soc., Providence, R.I., 1983, pp. 51–64. MR 711042
- —, Table of immersions and embeddings of real projective spaces, http://www.lehigh.edu/$\sim$dmd1/immtable
- Donald M. Davis, Computing $v_1$-periodic homotopy groups of spheres and some compact Lie groups, Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 993–1048. MR 1361905, DOI 10.1016/B978-044481779-2/50021-3
- Donald M. Davis and Mark E. Mahowald, The geometric dimension of some vector bundles over projective spaces, Trans. Amer. Math. Soc. 205 (1975), 295–315. MR 372854, DOI 10.1090/S0002-9947-1975-0372854-9
- S. Gitler and M. Mahowald, The geometric dimension of real stable vector bundles, Bol. Soc. Mat. Mexicana (2) 11 (1966), 85–107. MR 231367
- André Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv. 37 (1962/63), 155–176 (French). MR 157391, DOI 10.1007/BF02566970
- Mark Mahowald, On obstruction theory in orientable fiber bundles, Trans. Amer. Math. Soc. 110 (1964), 315–349. MR 157386, DOI 10.1090/S0002-9947-1964-0157386-8
- Mark Mahowald, The metastable homotopy of $S^{n}$, Memoirs of the American Mathematical Society, No. 72, American Mathematical Society, Providence, R.I., 1967. MR 0236923
- B. J. Sanderson, A non-immersion theorem for real projective space, Topology 2 (1963), 209–211. MR 151987, DOI 10.1016/0040-9383(63)90004-1
- Emery Thomas, Embedding manifolds in Euclidean space, Osaka Math. J. 13 (1976), no. 1, 163–186. MR 474332
- V. Zelov, Embeddings and immersions of real projective spaces, Ph.D. thesis, Lehigh University (1997).
Additional Information
- Donald M. Davis
- Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
- MR Author ID: 55085
- Email: dmd1@lehigh.edu
- Vitaly Zelov
- Affiliation: Microsoft Corporation, Charlotte, North Carolina
- Email: vitalyze@microsoft.com
- Received by editor(s): February 12, 1999
- Published electronically: June 14, 2000
- Communicated by: Ralph Cohen
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3731-3740
- MSC (1991): Primary 57R40
- DOI: https://doi.org/10.1090/S0002-9939-00-05444-7
- MathSciNet review: 1690981