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Riemann-Roch theorems for differentiable manifolds
Authors:
M. F. Atiyah and F. Hirzebruch
Journal:
Bull. Amer. Math. Soc. 65 (1959), 276-281
MathSciNet review:
0110106
Full-text PDF
References |
Additional Information
- 1.
M. F. Atiyah and F. Hirzebruch, Some non-embeddability theorems for differentiable manifolds, Colloque de Topologie, Lille, 1959.
- 2.
A.
Borel and F.
Hirzebruch, Characteristic classes and homogeneous spaces. I,
Amer. J. Math. 80 (1958), 458–538. MR 0102800
(21 #1586)
- 3.
Armand
Borel and Jean-Pierre
Serre, Le théorème de Riemann-Roch, Bull. Soc.
Math. France 86 (1958), 97–136 (French). MR 0116022
(22 #6817)
- 4.
Raoul
Bott, The stable homotopy of the classical groups, Proc. Nat.
Acad. Sci. U.S.A. 43 (1957), 933–935. MR 0102802
(21 #1588)
- 5.
Raoul
Bott, The space of loops on a Lie group, Michigan Math. J.
5 (1958), 35–61. MR 0102803
(21 #1589)
- 6.
R. Bott, Some remarks on the periodicity theorems, Colloque de Topologie, Lille, 1959.
- 7.
F.
Hirzebruch, Neue topologische Methoden in der algebraischen
Geometrie, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.),
Heft 9, Springer-Verlag, Berlin, 1956 (German). MR 0082174
(18,509b)
- 8.
Friedrich
Hirzebruch, Some problems on differentiable and complex
manifolds, Ann. of Math. (2) 60 (1954),
213–236. MR 0066013
(16,518c)
- 9.
I.
M. James and J.
H. C. Whitehead, The homotopy theory of sphere bundles over
spheres. I, Proc. London Math. Soc. (3) 4 (1954),
196–218. MR 0061838
(15,892b)
- 10.
M. A. Kervaire and J. Milnor, Bernoulli numbers, homotopy groups and a theorem of Rohlin. Proceedings of the International Congress of Mathematicians, 1958.
- 11.
J. Milnor, On the cobordisme ring Ω*, and a complex analogue, (in preparation).
- 12.
V.
A. Rohlin, New results in the theory of four-dimensional
manifolds, Doklady Akad. Nauk SSSR (N.S.) 84 (1952),
221–224 (Russian). MR 0052101
(14,573b)
- 13.
R.
Thom, Une théorie intrinsèque des puissances de
Steenrod, Colloque de Topologie de Strasbourg, 1951, no. VII, La
Bibliothèque Nationale et Universitaire de Strasbourg, 1952,
pp. 13 (French). MR 0051509
(14,491a)
- 14.
Wen-tsün
Wu, On Pontrjagin classes. III, Acta Math. Sinica
4 (1954), 323–346 (Chinese, with English summary).
MR
0080300 (18,225f)
- 1.
- M. F. Atiyah and F. Hirzebruch, Some non-embeddability theorems for differentiable manifolds, Colloque de Topologie, Lille, 1959.
- 2.
- A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math. vol. 80 (1958) pp. 458-538; II and III to appear. MR 102800
- 3.
- A. Borel and J-P. Serre, Le théorème de Riemann-Roch (d'après Grothendieck). Bull. Soc. Math. France vol. 86 (1958), pp. 97-136. MR 116022
- 4.
- R. Bott, The stable homotopy of the classical groups, Proc. Nat. Acad. Sci. U.S.A. vol. 43 (1957) pp. 933-935. MR 102802
- 5.
- R. Bott, The space of loops on a Lie group, Mich. Math. J. vol. 5 (1958) pp. 35-61. MR 102803
- 6.
- R. Bott, Some remarks on the periodicity theorems, Colloque de Topologie, Lille, 1959.
- 7.
- F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Springer, 1956. MR 82174
- 8.
- F. Hirzebruch, Some problems on differentiable and complex manifolds, Ann. of Math. vol. 60 (1954) pp. 213-236. MR 66013
- 9.
- I. M. James and J. H. C. Whitehead, The homotopy theory of sphere bundles over spheres, Proc. London Math. Soc. vol. 4 (1954) pp. 196-218. MR 61838
- 10.
- M. A. Kervaire and J. Milnor, Bernoulli numbers, homotopy groups and a theorem of Rohlin. Proceedings of the International Congress of Mathematicians, 1958.
- 11.
- J. Milnor, On the cobordisme ring Ω*, and a complex analogue, (in preparation).
- 12.
- V. A. Rohlin, New results in the theory of 4-dimensional manifolds, Dokl. Acad. Nauk. S.S.S.R. vol. 84 (1952) pp. 221-224 (in Russian). MR 52101
- 13.
- R. Thom, Espacés fibrès en sphères et carrés de Steenrod, Ann. Sci. École Norm. Sup. vol. 69 (1952) pp. 109-182. MR 51509
- 14.
- W. T. Wu, On the Pontrjagin classes III, Acta Math. Sinica vol. 4 (1954) (in Chinese). MR 80300
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1959-10344-X
PII:
S 0002-9904(1959)10344-X
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