Steenrod operations in subanalytic homology

Robert M. Hardt; Clint G. McCrory

Compositio Mathematica (1979)

  • Volume: 39, Issue: 3, page 333-371
  • ISSN: 0010-437X

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Hardt, Robert M., and McCrory, Clint G.. "Steenrod operations in subanalytic homology." Compositio Mathematica 39.3 (1979): 333-371. <http://eudml.org/doc/89423>.

@article{Hardt1979,
author = {Hardt, Robert M., McCrory, Clint G.},
journal = {Compositio Mathematica},
keywords = {subanalytic set; geometric homology operation; subanalytic chain; double point; branch point; Steenrod reduced squaring operations},
language = {eng},
number = {3},
pages = {333-371},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Steenrod operations in subanalytic homology},
url = {http://eudml.org/doc/89423},
volume = {39},
year = {1979},
}

TY - JOUR
AU - Hardt, Robert M.
AU - McCrory, Clint G.
TI - Steenrod operations in subanalytic homology
JO - Compositio Mathematica
PY - 1979
PB - Sijthoff et Noordhoff International Publishers
VL - 39
IS - 3
SP - 333
EP - 371
LA - eng
KW - subanalytic set; geometric homology operation; subanalytic chain; double point; branch point; Steenrod reduced squaring operations
UR - http://eudml.org/doc/89423
ER -

References

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  1. [1] A. Borel and A. Haefliger: La class d'homologie fondamentale d'un espace analytique. Bull. Soc. Math. France89 (1961) 461-513. Zbl0102.38502MR149503
  2. [2] A. Dold: Lectures on Algebraic Topology. Berlin- Heidelberg-New York: Springer1972. Zbl0234.55001MR415602
  3. [3] S. Eilenberg and N. Steenrod: Foundations of Algebraic Topology. Princeton: Princeton University Press1952. Zbl0047.41402MR50886
  4. [4] H. Federer: Geometric Measure Theory. Berlin- Heidelberg-New York: Springer1969. Zbl0176.00801MR257325
  5. [5] A.M. Gabriélov: Projections of semi-analytic sets. Funktsional' nyi analiz i ego prilozheniya2, no. 4 (1968) 18-30 [Functional analysis and its applications2, no. 4, 282-291 (1968)]. Zbl0179.08503MR245831
  6. [6] R.M. Hardt: Slicing and intersection theory for chains associated with real analytic varieties. Acta Math.129 (1972) 75-136. Zbl0234.32005MR315561
  7. [7] R.M. Hardt: Slicing and intersection theory for chains modulo v associated with real analytic varieties. Trans. Amer. Math. Soc.183 (1973) 327-340. Zbl0267.28010MR338430
  8. [8] R.M. Hardt: Homology theory for real analytic and semianalytic sets. Annali Sc. Norm. Sup. Pisa, s. 4,2, n.1, (1975) 107-148. Zbl0309.32004MR382699
  9. [9] R.M. Hardt: Stratification of real analytic mappings and images. Inventiones math.28 (1975) 193-208. Zbl0298.32003MR372237
  10. [10] R.M. Hardt: Topological properties of subanalytic sets. Trans. Amer. Math. Soc.211 (1975) 57-70. Zbl0303.32008MR379882
  11. [11] R.M. Hardt: Triangulation of subanalytic sets and proper light subanalytic maps. Inventiones Math.38 (1977) 207-217. Zbl0331.32006MR454051
  12. [12] R.M. Hardt: Homology and images of semianalytic sets. Bull. Amer. Math. Soc.80 (1974) 675-678. Zbl0291.32011MR348140
  13. [13] D. Hilbert and S. Cohn-Vossen: Geometry and the Imagination. New York: Chelsea1952. Zbl0047.38806MR46650
  14. [14] H. Hironaka: Subanalytic sets. In: Number Theory, Algebraic Geometry, and Commutative Algebra in honor of Y. Akizuki, pp. 453-493. Tokyo: Kinokuniya Publications1973. Zbl0297.32008MR377101
  15. [15] H. Hironaka: Triangulations of algebraic sets. In: Proceedings of Symposia in Pure Mathematics, Amer. Math. Soc.29 (1975) 165-185. Zbl0332.14001MR374131
  16. [16] J.F.P. Hudson: Piecewise Linear Topology. New York: Benjamin1969. Zbl0189.54507MR248844
  17. [17] S. Kleiman: The enumerative geometry of singularities. In: Real and Complex Singularities, Oslo1976, Sijthoff & Noordhoff International Publishers. 
  18. [18] C.G. Mccrory: Geometric homology operations. Studies in Algebraic Topology, Advances in Mathematics Supplementary Studies, 5 (1978) 119-141. Zbl0454.55014MR527247
  19. [19] R. Macpherson: Chern classes for singular algebraic varieties. Ann. of Math.100 (1974) 423-432. Zbl0311.14001MR361141
  20. [20] J. Milnor and J. Stasheff: Characteristic Classes. Annals of Math. Study76. Princeton: Princeton University Press1974. Zbl0298.57008MR440554
  21. [21] F. Ronga: La classe duale aux points doubles d'une application. Compositio Math.27 (1973) 223-232. Zbl0271.57009MR391114
  22. [22] N. Steenrod and D. Epstein: Cohomology Operations. Annals of Math. Study50. Princeton: Princeton University Press1962. Zbl0102.38104MR145525
  23. [23] D. Sullivan: Combinatorial invariants of analytic spaces. In: Proceedings of the Liverpool Singularities Symposium I, Springer Lecture Notes in Math. 192. Berlin-Heidelberg-New York: Springer1971. Zbl0227.32005MR278333
  24. [24] R. Thom: Espaces fibrés en sphères et carrés de Steenrod. Annali. Sc. Norm. Sup.69 (3), (1952) 109-181. Zbl0049.40001MR54960
  25. [25] R. Thom: Les singularités des applications différentiables. Ann. Inst. Fourier6, (1956) 43-87. Zbl0075.32104MR87149
  26. [26] W.-T. Wu:A Theory of Imbedding, Immersion, and Isotopy of Polytopes in a Euclidean Space. Peking: Science Press1965. Zbl0177.26402MR215305
  27. [27] C. Weber: ∈- Applications dans une variété. Comm. Math. Helv.49 (1974) 125-135. Zbl0291.54011
  28. [28] E.C. Zeeman: Seminar on Combinatorial Topology. Inst. Hautes Études Sci., Bures-Sur-Yvette, and the University of Warwick at Coventry, 1963-66. 

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