Poincaré embedding of the diagonal
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- by Yanghyun Byun
- Trans. Amer. Math. Soc. 350 (1998), 3537-3553
- DOI: https://doi.org/10.1090/S0002-9947-98-02274-0
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Abstract:
There is a Poincaré embedding structure on the diagonal $X\rightarrow X\times X$ under the conditions: i) $X$ is formed by gluing two compact smooth manifolds along their boundaries using a homotopy equivalence and ii) a square-root closed condition is satisfied by the fundamental groupoid of the boundary.References
- René Benlian and John Wagoner, Type d’homotopie fibré et réduction structurale des fibrés vectoriels, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), A207–A209 (French). MR 221524
- Sylvain E. Cappell, A splitting theorem for manifolds, Invent. Math. 33 (1976), no. 2, 69–170. MR 438359, DOI 10.1007/BF01402340
- André Haefliger, Plongements différentiables de variétés dans variétés, Comment. Math. Helv. 36 (1961), 47–82 (French). MR 145538, DOI 10.1007/BF02566892
- Jean-Claude Hausmann and Pierre Vogel, Geometry on Poincaré spaces, Mathematical Notes, vol. 41, Princeton University Press, Princeton, NJ, 1993. MR 1238937
- J. P. E. Hodgson, The Whitney technique for Poincaré complex embeddings, Proc. Amer. Math. Soc. 35 (1972), 263–268. MR 303543, DOI 10.1090/S0002-9939-1972-0303543-7
- Lowell Jones, Patch spaces: a geometric representation for Poincaré spaces, Ann. of Math. (2) 97 (1973), 306–343. MR 315720, DOI 10.2307/1970849
- J.R. Klein, W. Richter and Shmuel Weinberger, A below middle dimension simply connected Poincaré Whitney embedding theorem, (to appear)
- Norman Levitt, Applications of Poincaré duality spaces to the topology of manifolds, Topology 11 (1972), 205–221. MR 295353, DOI 10.1016/0040-9383(72)90008-0
- Renzo A. Piccinini, Lectures on homotopy theory, North-Holland Mathematics Studies, vol. 171, North-Holland Publishing Co., Amsterdam, 1992. MR 1150242
- Volker Puppe, A remark on “homotopy fibrations”, Manuscripta Math. 12 (1974), 113–120. MR 365556, DOI 10.1007/BF01168646
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210112
- C. T. C. Wall, Poincaré complexes. I, Ann. of Math. (2) 86 (1967), 213–245. MR 217791, DOI 10.2307/1970688
- C. T. C. Wall, Surgery on compact manifolds, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR 0431216
- George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508, DOI 10.1007/978-1-4612-6318-0
- Albert Eagle, Series for all the roots of a trinomial equation, Amer. Math. Monthly 46 (1939), 422–425. MR 5, DOI 10.2307/2303036
Bibliographic Information
- Yanghyun Byun
- Affiliation: Department of Mathematics, Hanyang University, Seongdong-Gu, Seoul, Korea
- Email: yhbyun@fermat.hanyang.ac.kr
- Received by editor(s): July 29, 1996
- Additional Notes: Partially supported by 1996 Faculty Research Fund of Hanyang University, Korea.
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 3537-3553
- MSC (1991): Primary 57P10
- DOI: https://doi.org/10.1090/S0002-9947-98-02274-0
- MathSciNet review: 1491856