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René Thom's work on geometric homology and bordism


Author: Dennis Sullivan
Journal: Bull. Amer. Math. Soc. 41 (2004), 341-350
MSC (2000): Primary 55-XX, 14-XX, 57-XX
Published electronically: April 13, 2004
MathSciNet review: 2058291
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  • [1] René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 0061823
  • [2] René Thom, Espaces fibrés en sphères et carrés de Steenrod, Ann. Sci. Ecole Norm. Sup. (3) 69 (1952), 109–182 (French). MR 0054960
  • [3] Pontryagin, L., Doklady Akad Nauk SSSR 34 (1942) pp. 35-37.
  • [4] William Browder, Surgery on simply-connected manifolds, Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65. MR 0358813
  • [5] Novikov, S.P., ``Homotopy equivalent smooth manifolds", Translations of Amer. Math. Soc. 48 (1965) pp. 271-396.
  • [6] C. T. C. Wall, Surgery on compact manifolds, Academic Press, London-New York, 1970. London Mathematical Society Monographs, No. 1. MR 0431216
  • [7] M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. of Math. (2) 87 (1968), 484–530. MR 0236950
  • [8] Madsen, I., and Weiss, M., ``Proof of Mumford's conjecture" (authors' web page).
  • [9] Dennis Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. (2) 100 (1974), 1–79. MR 0442930
  • [10] R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969), 240–284 (French). MR 0239613, 10.1090/S0002-9904-1969-12138-5
  • [11] D. Sullivan, Singularities in spaces, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Springer, Berlin, 1971, pp. 196–206. Lecture Notes in Math., Vol. 209. MR 0339241
  • [12] Hironaka, H., ``Resolutions of the singularities of an algebraic variety in characteristic zero", Ph.D. Thesis, Harvard University (1963).
  • [13] Robert Wells, Cobordism groups of immersions, Topology 5 (1966), 281–294. MR 0196760
  • [14] Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR 0148075
  • [15] Jeff Cheeger, On the Hodge theory of Riemannian pseudomanifolds, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 91–146. MR 573430
  • [16] John W. Morgan and Dennis P. Sullivan, The transversality characteristic class and linking cycles in surgery theory, Ann. of Math. (2) 99 (1974), 463–544. MR 0350748
  • [17] Mark Goresky and Robert MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. MR 572580, 10.1016/0040-9383(80)90003-8
  • [18] Klaus Jänich, Charakterisierung der Signatur von Mannigfaltigkeiten durch eine Additivitätseigenschaft, Invent. Math. 6 (1968), 35–40 (German). MR 0231399
  • [19] Singer, I.M., ``Prospects in Math", Princeton series (1970).
  • [20] Sullivan, D., ``The signature, geometric cycles, and K-theory", unpublished manuscript, 1973-74; and see [30].
  • [21] Morava, J., ``Extraordinary cohomology theories and K-theory" (author's web page).
  • [22] Hopkins, M., ``Algebraic Topology and Modular Forms", Proceedings of International Congress of Mathematicians, Vol. 1 (Beijing 2002), pp. 291-317, Higher Ed. Press, Beijing, 2002.
  • [23] Dennis Sullivan, Geometric periodicity and the invariants of manifolds, Manifolds–Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, 1971, pp. 44–75. MR 0285012
  • [24] J. Frank Adams, Stable homotopy theory, Lectures delivered at the University of California at Berkeley, vol. 1961, Springer-Verlag, Berlin-Göttingen-Heidelberg-New York, 1964. MR 0185597
  • [25] Friedrich Hirzebruch, Topological methods in algebraic geometry, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Translated from the German and Appendix One by R. L. E. Schwarzenberger; With a preface to the third English edition by the author and Schwarzenberger; Appendix Two by A. Borel; Reprint of the 1978 edition. MR 1335917
  • [26] Weyl, H., Analisis situs combinatorio. Revista Mat. Hispano-Americana, vols. 5-6 (1923-24); reproduced in Ges. Abh., vol. II, pp. 58-59.
  • [27] André Weil, Scientific works. Collected papers. Vol. II (1951–1964), Springer-Verlag, New York-Heidelberg, 1979 (French). MR 537935
  • [28] Nobuaki Yagita, On the algebraic structure of cobordism operations with singularities, J. London Math. Soc. (2) 16 (1977), no. 1, 131–141. MR 0445492
  • [29] Boris I. Botvinnik, Manifolds with singularities and the Adams-Novikov spectral sequence, London Mathematical Society Lecture Note Series, vol. 170, Cambridge University Press, Cambridge, 1992. MR 1192127
  • [30] P. H. Siegel, Witt spaces: a geometric cycle theory for 𝐾𝑂-homology at odd primes, Amer. J. Math. 105 (1983), no. 5, 1067–1105. MR 714770, 10.2307/2374334
  • [31] S. Buoncristiano, C. P. Rourke, and B. J. Sanderson, A geometric approach to homology theory, Cambridge University Press, Cambridge-New York-Melbourne, 1976. London Mathematical Society Lecture Note Series, No. 18. MR 0413113
  • [32] S. S. Chern, F. Hirzebruch, and J.-P. Serre, On the index of a fibered manifold, Proc. Amer. Math. Soc. 8 (1957), 587–596. MR 0087943, 10.1090/S0002-9939-1957-0087943-0

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Additional Information

Dennis Sullivan
Affiliation: City College (CUNY), 365 Fifth Avenue, New York, New York 10016
Email: dsullivan@gc.cuny.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-04-01026-2
Received by editor(s): February 24, 2004
Published electronically: April 13, 2004
Article copyright: © Copyright 2004 American Mathematical Society