Local blow-up of stratified sets up to bordism
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- by S. Buoncristiano and M. Dedò PDF
- Trans. Amer. Math. Soc. 273 (1982), 253-280 Request permission
Abstract:
Homological obstructions are given, whose vanishing is a necessary and sufficient condition for the existence of a blow-up of an abstract prestratification $V$ along a ’locally top-dimensional’ substratification $V’$.References
-
S. Akbulut and H. C. King, Real algebraic structures on some topological spaces, Univ. of Maryland, preprint, 1979.
- Nils Andreas Baas, Bordism theories with singularities, Proceedings of the Advanced Study Institute on Algebraic Topology (Aarhus Univ., Aarhus, 1970) Various Publ. Ser., No. 13, Mat. Inst., Aarhus Univ., Aarhus, 1970, pp. 1–16. MR 0346823
- S. Buoncristiano and M. Dedò, On resolving singularities and relating bordism to homology, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), no. 4, 605–624. MR 600525
- S. Buoncristiano, C. P. Rourke, and B. J. Sanderson, A geometric approach to homology theory, London Mathematical Society Lecture Note Series, No. 18, Cambridge University Press, Cambridge-New York-Melbourne, 1976. MR 0413113
- P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 33, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR 0176478
- Mitsuyoshi Kato, Topological resolution of singularities, Topology 12 (1973), 355–372. MR 339196, DOI 10.1016/0040-9383(73)90028-1
- Mitsuyoshi Kato, Partial Poincaré duality for $k$-regular spaces and complex algebraic sets, Topology 16 (1977), no. 1, 33–50. MR 450607, DOI 10.1016/0040-9383(77)90029-5 J. Mather, Notes on topological stability, Lecture Notes, Harvard Univ., 1970.
- John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
- David A. Stone, Stratified polyhedra, Lecture Notes in Mathematics, Vol. 252, Springer-Verlag, Berlin-New York, 1972. MR 0372870 R. E. Stong, Notes on cobordism theory, Math. Notes, Princeton Univ. Press, Princeton, N. J., 1968.
- R. E. Stong, Some remarks on symplectic cobordism, Ann. of Math. (2) 86 (1967), 425–433. MR 219079, DOI 10.2307/1970608
- D. Sullivan, Singularities in spaces, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Lecture Notes in Math., Vol. 209, Springer, Berlin, 1971, pp. 196–206. MR 0339241
- R. Thom, Stratified sets and morphisms: local models, Proceedings of Liverpool Singularities—Symposium, I (1969/70), Lecture Notes in Mathematics, Vol. 192, Springer, Berlin, 1971, pp. 153–164. MR 0283808
- René Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86 (French). MR 61823, DOI 10.1007/BF02566923
- R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969), 240–284 (French). MR 239613, DOI 10.1090/S0002-9904-1969-12138-5
- Andrei Verona, Homological properties of abstract prestratifications, Rev. Roumaine Math. Pures Appl. 17 (1972), 1109–1121. MR 322887
- Norman Levitt, Exotic singular structures on spheres, Trans. Amer. Math. Soc. 205 (1975), 371–388. MR 377909, DOI 10.1090/S0002-9947-1975-0377909-0
- Arunas Liulevicius, Notes on homotopy of Thom spectra, Amer. J. Math. 86 (1964), 1–16. MR 166787, DOI 10.2307/2373032
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 273 (1982), 253-280
- MSC: Primary 58A35; Secondary 57R90
- DOI: https://doi.org/10.1090/S0002-9947-1982-0664041-5
- MathSciNet review: 664041