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Some new embeddings and nonimmersions of real projective spaces


Authors: Donald M. Davis and Vitaly Zelov
Journal: Proc. Amer. Math. Soc. 128 (2000), 3731-3740
MSC (1991): Primary 57R40
DOI: https://doi.org/10.1090/S0002-9939-00-05444-7
Published electronically: June 14, 2000
MathSciNet review: 1690981
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. L. Astey and D. M. Davis, Nonimmersions of real projective spaces implied by $BP$, Bol Soc Mat Mex 24 (1979) 49-55.
  • 2. D. M. Davis, Some new immersions and nonimmersions of real projective spaces, AMS Contemporary Math 19 (1983) 51-64. MR 84k:57016
  • 3. -, Table of immersions and embeddings of real projective spaces, http://www.lehigh.edu/$\sim$dmd1/immtable
  • 4. -, Computing $v_1$-periodic homotopy groups of spheres and certain compact Lie groups, Handbook of Algebraic Topology, Elsevier (1995) 993-1049. MR 97g:55017
  • 5. D. M. Davis and M. Mahowald, The geometric dimension of some vector bundles over projective spaces, Trans Amer Math Soc 205 (1975) 295-315. MR 51:9058
  • 6. S. Gitler and M. E. Mahowald, The geometric dimension of real stable vector bundles, Bol Soc Mat Mex 11 (1966) 85-107. MR 37:6922
  • 7. A. Haefliger, Plongements différentiable dans le domaine stable, Comm Math Helv 37 (1962) 155-176. MR 28:625
  • 8. M. E. Mahowald, On obstruction theory in orientable fibre bundles, Trans Amer Math Soc 110 (1964) 315-349. MR 28:620
  • 9. -, The metastable homotopy of $S^n$, Mem Amer Math Soc 72 (1967). MR 38:5216
  • 10. B. J. Sanderson, A nonimmersion theorem for real projective space, Topology 2 (1963) 209-211. MR 27:1968
  • 11. E. Thomas, Embedding manifolds in Euclidean space, Osaka Jour Math 13 (1976) 163-186. MR 57:13978
  • 12. V. Zelov, Embeddings and immersions of real projective spaces, Ph.D. thesis, Lehigh University (1997).

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Additional Information

Donald M. Davis
Affiliation: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Email: dmd1@lehigh.edu

Vitaly Zelov
Affiliation: Microsoft Corporation, Charlotte, North Carolina
Email: vitalyze@microsoft.com

DOI: https://doi.org/10.1090/S0002-9939-00-05444-7
Keywords: Embeddings, immersions, real projective spaces, obstruction theory
Received by editor(s): February 12, 1999
Published electronically: June 14, 2000
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society

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