Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0273-0979-04-01026-2
Published electronically: April 13, 2004
MathSciNet review: 2058291
Full-text PDF

References | Similar Articles | Additional Information

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

  • [1] Thom, R., ``Quelques proprietes globales des varietes differentiables", Comm. Math. Helv. 28 (1954) 17-86. MR 15:890a
  • [2] Thom, R., ``Espaces fibres en spheres et carres de Steenrod", Ann. Sci. Ecole Norm. Sup. (3) 69 (1952); and ``Les classes caracteristiques de Pontryagin des varietes triangulees", Symp. Int. de Top. Alg. UNESCO (1959) p. 40. MR 14:1004c
  • [3] Pontryagin, L., Doklady Akad Nauk SSSR 34 (1942) pp. 35-37.
  • [4] Browder, W., ``Surgery on Simply Connected Manifolds", Ergebnisse Series 65, Springer (1972). MR 50:11272
  • [5] Novikov, S.P., ``Homotopy equivalent smooth manifolds", Translations of Amer. Math. Soc. 48 (1965) pp. 271-396.
  • [6] Wall, C.T.C., ``Surgery on Compact Manifolds", Academic Press, 1970. MR 55:4217
  • [7] Atiyah, M.F., and Singer, I.M., ``The index of elliptic operators: I", Annals of Mathematics, 2nd Ser., vol. 87, no. 3. (May 1968), pp. 484-530. MR 38:5243
  • [8] Madsen, I., and Weiss, M., ``Proof of Mumford's conjecture" (authors' web page).
  • [9] Sullivan, D., ``Genetics of homotopy theory and the Adams conjecture", Annals of Math. 100, no. 1 (1974) 1-79. MR 56:1305
  • [10] Thom, R., ``Ensembles et morphismes stratifies", Bull. Amer. Math. Soc. 75 (1969) 240-284. MR 39:970
  • [11] Sullivan, D., ``Singularities in spaces", Proceedings of Liverpool Singularities Symposium (1970), Vol. II, Springer Lecture Notes 209, 1971, pp. 196-206. MR 49:4002
  • [12] Hironaka, H., ``Resolutions of the singularities of an algebraic variety in characteristic zero", Ph.D. Thesis, Harvard University (1963).
  • [13] Wells, Robert, ``Cobordism groups of immersions", Topology 5, pp. 281-294 (1966). MR 33:4946
  • [14] Milnor, J. (and Kervaire, M.), ``Groups of homotopy spheres. I'', Ann. of Math. 77 (1963) pp. 504-537. MR 26:5584
  • [15] Cheeger, Jeff, ``On the Hodge Theory of Riemannian pseudomanifolds", Amer. Math. Soc., Proc. Sym. Pure Math. XXXVI (1980) 91-146; and with Goresky and MacPherson, ``$L^2$ cohomology and intersection homology of singular algebraic varieties", Seminar on Differential Geometry, Yau S.T. (ed.), Princeton Univ. Press, Princeton, NJ, 1982. MR 83a:58081
  • [16] Morgan, J., and Sullivan, D., ``Transversality characteristic class and linking cycles in surgery theory", Annals of Math. 99 (1974) 463-544. MR 50:3240
  • [17] Goresky, M., and MacPherson, R., ``Intersection homology theory", Topology 19 (1980) pp. 135-162; and ``Intersection homology II", Inventiones Math. 72 (or 71) pp. 77-130. MR 82b:57010
  • [18] Novikov, S.P., ``Additivity of the signature of manifolds with boundary" (author's web page); and K. Janich, ``Characterisierung der signature von Mannifaltijkeiten durch eine Additivitats Eigenschaft", Inventiones Math. 6 (1968) 35-40. MR 37:6954
  • [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] Sullivan, D., ``Geometric Periodicity and the Invariants of Manifolds" Manifolds, Amsterdam, 1970, Lecture Notes, Springer-Verlag, 197 (1970) 44-75. Also, ``Galois Symmetry in Manifolds Theory at the Primes", Proc. ICM, Nice, Part 2 (1970) 169-175. MR 44:2236
  • [24] Adams, J. Frank, ``Stable homotopy theory", lectures delivered at University of California at Berkeley, 1961, Lecture Notes, Springer-Verlag, vol. 3 (notes by Al Vasquez), 1964. MR 32:3061
  • [25] Hirzebruch, F., ``New Topological Methods in Algebraic Geometry", Springer-Verlag, 1956. MR 96c:57002
  • [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] Weil, A., ``Collected Papers'', Vol. II, pp. 555-556; or Amer. J. Math. 79 (1957) pp. 951-952. Correspondence by XXX. MR 80k:01067b
  • [28] Yagita, N., ``Algebraic structure of cobordism operations with singularities" and ``On the Steenrod algebra of Morava K-theory", J. London Math. Soc. (1977), vol. 16, pp. 131-141; and J. London Math. Soc. (1980), vol. 22, pp. 423-438. MR 56:3832
  • [29] Botvinnik, B., ``Manifolds with singularities and the Adams-Novikov spectral sequence", London Math. Soc. Lecture Notes Series, 170, Cambridge University Press, 1992. MR 93h:55002
  • [30] Siegel, P., ``Witt spaces: a geometric cycle theory for $K{\mathrm O}$-homology at odd primes'', Amer. J. Math., vol. 105, no. 5, pp. 1067-1105, October 1983. MR 85f:57011
  • [31] Buoncristiano, S., Rourke, C.P., and Sanderson, B.J., ``A Geometric Approach to Homology Theory", London Math. Soc. Lecture Note Series, 18, Cambridge University Press, 1976. MR 54:1234
  • [32] Chern, S.S., Hirzebruch, F., and Serre, J-P. ``On the index of a fibered manifold", Proc. Amer. Math. Soc. 8 (1957), 587-596. MR 19:441c

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 55-XX, 14-XX, 57-XX

Retrieve articles in all journals with MSC (2000): 55-XX, 14-XX, 57-XX


Additional Information

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

DOI: https://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

American Mathematical Society