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Some immersion theorems for projective spaces


Author: A. Duane Randall
Journal: Trans. Amer. Math. Soc. 147 (1970), 135-151
MSC: Primary 57.30
DOI: https://doi.org/10.1090/S0002-9947-1970-0253357-4
MathSciNet review: 0253357
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  • [1] J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. (2) 72 (1960), 20-104. MR 25 #4530. MR 0141119 (25:4530)
  • [2] J. Adem, Sobre operaciones cohomologicas secundarias, Bol. Soc. Mat. Mexicana (2) 7 (1962), 95-110. MR 29 #5243. MR 0167978 (29:5243)
  • [3] J. Adem and S. Gitler, Secondary characteristic classes and the immersion problem, Bol. Soc. Mat. Mexicana (2) 8 (1963), 53-78. MR 29 #5255. MR 0167990 (29:5255)
  • [4] -, Non-immersion theorems for real projective spaces, Bol. Soc. Mat. Mexicana (2) 9 (1964), 37-50. MR 32 #461. MR 0182979 (32:461)
  • [5] M. Atiyah, Thom complexes, Proc. London Math. Soc. (3) 11 (1961), 291-310. MR 24 #A1727. MR 0131880 (24:A1727)
  • [6] S. Feder, Non-immersion theorems for complex and quaternionic projective spaces, Bol. Soc. Mat. Mexicana (2) 11 (1966), 62-67. MR 38 #721. MR 0232396 (38:721)
  • [7] S. Gitler, The projective Stiefel manifolds. II: Applications, Topology 7 (1968), 47-53. MR 36 #3373b. MR 0220308 (36:3373b)
  • [8] S. Gitler and M. Mahowald, Geometric dimension of real stable vector bundles, Bol. Soc. Mat. Mexicana (2) 11 (1966), 85-107. MR 37 #6922. MR 0231367 (37:6922)
  • [9] -, The immersion of manifolds, Bull. Amer. Math. Soc. 73 (1967), 696-700. MR 35 #4940. MR 0214089 (35:4940)
  • [10] S. Gitler, M. Mahowald and R. J. Milgram, Secondary cohomology operations and complex vector bundles, Proc. Amer. Math. Soc. 22 (1969), 223-229. MR 0243515 (39:4836)
  • [11] -, The nonimmersion problem for $ R{P^n}$ and higher-order cohomology operations, Proc. Nat. Acad. Sci. U.S.A. 60 (1968), 432-437. MR 37 #3581. MR 0227997 (37:3581)
  • [12] M. Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959), 242-276. MR 22 #9980. MR 0119214 (22:9980)
  • [13] C. S. Hoo and M. Mahowald, Some homotopy groups of Stiefel manifolds, Bull. Amer. Math. Soc. 71 (1965), 661-667. MR 31 #1675. MR 0177412 (31:1675)
  • [14] A. Hughes and E. Thomas, A note on certain secondary cohomology operations, Bol. Soc. Mat. Mexicana (1) 13 (1968), 1-17. MR 0266203 (42:1110)
  • [15] D. Husemoller, Fibre bundles, McGraw-Hill, New York, 1966. MR 37 #4821. MR 0229247 (37:4821)
  • [16] I. M. James, On the immersion problem for real projective spaces, Bull. Amer. Math. Soc. 69 (1963), 231-238. MR 26 #1900. MR 0144355 (26:1900)
  • [17] M. Mahowald, On obstruction theory in orientable fiber bundles, Trans. Amer. Math. Soc. 110 (1964), 315-349. MR 28 #620. MR 0157386 (28:620)
  • [18] -, Some Whitehead products in $ {S^n}$, Topology 4 (1965), 17-26. MR 31 #2724. MR 0178467 (31:2724)
  • [19] M. Mahowald and F. Peterson, Secondary cohomology operations on the Thorn class, Topology 2 (1963), 367-377. MR 28 #612. MR 0157378 (28:612)
  • [20] C. R. F. Maunder, Cohomology operations of the $ N$th kind, Proc. London Math. Soc. (31) 13 (1963), 125-154. MR 35 #2279. MR 0211398 (35:2279)
  • [21] R. J. Milgram, Immersing projective spaces, Ann. of Math. (2) 85 (1967), 473-482. MR 35 #2293. MR 0211412 (35:2293)
  • [22] G. Paechter, The groups $ {\pi _r}({V^{n,m}})$. I, Quart. J. Math. Oxford Ser. (2) 7 (1956), 249-268. MR 24 #A1725. MR 0131878 (24:A1725)
  • [23] A. D. Randall, Some immersions of manifolds (to appear)
  • [24] B. Sanderson, Immersions and embeddings of projective spaces, Proc. London Math. Soc. (3) 14 (1964), 137-153. MR 29 #2814. MR 0165532 (29:2814)
  • [25] J.-P. Serre, Cohomologie modulo 2 des complexes d'Eilenberg-MacLane, Comment. Math. Helv. 27 (1953), 198-232. MR 15, 643. MR 0060234 (15:643c)
  • [26] E. Thomas, Seminar on fiber spaces, Lecture Notes in Math., no. 13, Springer-Verlag, Berlin, 1966. MR 34 #3582. MR 0203733 (34:3582)
  • [27] E. Thomas, Postnikov invariants and higher order cohomology operations, Ann. of Math. (2) 85 (1967), 184-217. MR 35 #1029. MR 0210135 (35:1029)
  • [28] -, Real and complex vector fields on manifolds, J. Math. Mech. 16 (1967), 1183-1205. MR 35 #1030. MR 0210136 (35:1030)
  • [29] -, The index of a tangent $ 2$-field, Comment. Math. Helv. 42 (1967), 86-110. MR 35 #6158. MR 0215317 (35:6158)
  • [30] -, The span of a manifold, Quart. J. Math. Oxford Ser. (2) 19 (1968), 225-244. MR 38 #2804. MR 0234487 (38:2804)
  • [31] G. Walker and J. F. Adams, On complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 61 (1965), 81-103. MR 30 #1516. MR 0171285 (30:1516)

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DOI: https://doi.org/10.1090/S0002-9947-1970-0253357-4
Article copyright: © Copyright 1970 American Mathematical Society

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