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Transactions of the American Mathematical Society

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Topological properties of subanalytic sets

Author: Robert M. Hardt
Journal: Trans. Amer. Math. Soc. 211 (1975), 57-70
MSC: Primary 32B20; Secondary 32C05
MathSciNet review: 0379882
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Abstract: The stratification of a semianalytic or subanalytic set (that is, a set which locally is the proper analytic image of some semianalytic set) leads easily, by consecutive projections in Euclidean space, to a CW decomposition. In the category of subanalytic sets and continuous maps with subanalytic graphs, theories of slicing, intersection, and homology result through use of the topological chains defined by subanalytic sets.

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  • [1] A. Dold, Lectures on algebraic topology, Springer-Verlag, Berlin and New York, 1973.
  • [2] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325
  • [3] Burghart Giesecke, Simpliziale Zerlegung abzählbarer analytischer Räume, Math. Z. 83 (1964), 177–213 (German). MR 0159346
  • [4] Robert M. Hardt, Slicing and intersection theory for chains associated with real analytic varieties, Acta Math. 129 (1972), 75–136. MR 0315561
  • [5] -, Slicing and intersection theory for chains modulo v associated with real analytic varieties, Trans. Amer. Math. Soc. 185 (1973), 327-340.
  • [6] Robert M. Hardt, Homology theory for real analytic and semianalytic sets, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 2 (1975), no. 1, 107–148. MR 0382699
  • [7] Robert M. Hardt, Stratification of real analytic mappings and images, Invent. Math. 28 (1975), 193–208. MR 0372237
  • [8] Robert M. Hardt, Sullivan’s local Euler characteristic theorem, Manuscripta Math. 12 (1974), 87–92. MR 0338431
  • [9] Heisuke Hironaka, Subanalytic sets, Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki, Kinokuniya, Tokyo, 1973, pp. 453–493. MR 0377101
  • [10] S. Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa (3) 18 (1964), 449–474. MR 0173265
  • [11] -, Ensembles semianalytiques, Cours Faculté des Sciences d'Orsay, Inst. Hautes Études Sci. Bures-sur-Yvette, 1965.
  • [12] William F. Pohl, Some integral formulas for space curves and their generalization, Amer. J. Math. 90 (1968), 1321–1345. MR 0238247
  • [13] Robert M. Hardt, Triangulation of subanalytic sets and proper light subanalytic maps, Invent. Math. 38 (1976/77), no. 3, 207–217. MR 0454051

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Keywords: Stratification, semianalytic, subanalytic, subanalytic chain, slice, intersection
Article copyright: © Copyright 1975 American Mathematical Society