Triangulations of subanalytic sets and locally subanalytic manifolds
HTML articles powered by AMS MathViewer
- by M. Shiota and M. Yokoi
- Trans. Amer. Math. Soc. 286 (1984), 727-750
- DOI: https://doi.org/10.1090/S0002-9947-1984-0760983-2
- PDF | Request permission
Abstract:
If two polyhedrons are locally subanalytically homeomorphic (that is, the graph is locally subanalytic), they are ${\text {PL}}$ homeomorphic. A locally subanalytic manifold is one whose coordinate transformations are locally subanalytic. It is proved that a locally subanalytic manifold has a unique ${\text {PL}}$ manifold structure. A semialgebraic manifold also is considered.References
- R. D. Edwards, The double suspension of a certain homology $3$-sphere is ${S^5}$ (unpublished).
- Christopher G. Gibson, Klaus Wirthmüller, Andrew A. du Plessis, and Eduard J. N. Looijenga, Topological stability of smooth mappings, Lecture Notes in Mathematics, Vol. 552, Springer-Verlag, Berlin-New York, 1976. MR 0436203
- Robert M. Hardt, Triangulation of subanalytic sets and proper light subanalytic maps, Invent. Math. 38 (1976/77), no. 3, 207–217. MR 454051, DOI 10.1007/BF01403128
- Heisuke Hironaka, Subanalytic sets, Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki, Kinokuniya, Tokyo, 1973, pp. 453–493. MR 0377101
- Heisuke Hironaka, Triangulations of algebraic sets, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 165–185. MR 0374131
- S. Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 18 (1964), 449–474. MR 173265 —, Ensembles semi-analytique, Inst. Hautes Etudes Sci., Paris, 1965.
- John N. Mather, Stratifications and mappings, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic Press, New York, 1973, pp. 195–232. MR 0368064
- Barry Mazur, A note on some contractible $4$-manifolds, Ann. of Math. (2) 73 (1961), 221–228. MR 125574, DOI 10.2307/1970288
- John Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math. (2) 74 (1961), 575–590. MR 133127, DOI 10.2307/1970299
- James R. Munkres, Elementary differential topology, Annals of Mathematics Studies, No. 54, Princeton University Press, Princeton, N.J., 1963. Lectures given at Massachusetts Institute of Technology, Fall, 1961. MR 0163320
- Colin Patrick Rourke and Brian Joseph Sanderson, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin-New York, 1982. Reprint. MR 665919
- M. G. Scharlemann and L. C. Siebenmann, The Hauptvermutung for smooth singular homeomorphisms, Manifolds—Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973) Univ. Tokyo Press, Tokyo, 1975, pp. 85–91. MR 0372871
- Masahiro Shiota, Classification of Nash manifolds, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 3, 209–232 (English, with French summary). MR 723954 —, Piecewise linearization of real analytic functions, Publ. RIMS, Kyoto Univ. (to appear).
- L. C. Siebenmann, Topological manifolds, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 133–163. MR 0423356
- Jean-Louis Verdier, Stratifications de Whitney et théorème de Bertini-Sard, Invent. Math. 36 (1976), 295–312 (French). MR 481096, DOI 10.1007/BF01390015
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 286 (1984), 727-750
- MSC: Primary 32B20; Secondary 57Q15
- DOI: https://doi.org/10.1090/S0002-9947-1984-0760983-2
- MathSciNet review: 760983