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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

Poincaré embedding of the diagonal

Author(s): Yanghyun Byun
Journal: Trans. Amer. Math. Soc. 350 (1998), 3537-3553.
MSC (1991): Primary 57P10
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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:

1.
R. Benlian et J. Wagoner, Type d'homotopie fibré et réduction structurale des fibrés vetoriels, C.R. Acad. Sci. Paris Sér. A-B 265 (1967), A 205 - A 209 MR 36:4576

2.
S.E. Cappell, A splitting theorem for manifolds, Inventiones Math. 33 (1976), 69-17 MR 55:11274

3.
A. Haefliger, Plongements différentiables de variétés dans variétés, Comment. Math. Helv. 36 (1961), 47-82 MR 26:3069

4.
J.C. Hausmann and P. Vogel, Geometry on Poincaré spaces, Mathematical notes, Princeton University Press (1993) MR 95a:57042

5.
J.P.E. Hodgson, The Whitney technique for Poincaré complex embeddings, Proc. AMS 35 (1972), 263-268 MR 46:2680

6.
L. Jones, Patch spaces: a geometric representation for Poincaré spaces, Annals of Math. 97 (1973), 306-343; 102 (1975), 183-185. MR 47:4269, MR 52:11930

7.
J.R. Klein, W. Richter and Shmuel Weinberger, A below middle dimension simply connected Poincaré Whitney embedding theorem, (to appear)

8.
N. Levitt, Applications of Poincaré duality spaces to the topology of manifolds, Topology 11 (1972), 205-221 MR 45:4419

9.
R.A. Piccinini, Lectures on homotopy theory, Mathematics Studies 171, North-Holland (1992) MR 93e:55001

10.
V. Puppe, A remark on ``homotopy fibrations'', Manuscripta Math. 12 (1974), 113-120 MR 51:1808

11.
E.H. Spanier, Algebraic topology, McGraw-Hill, New York (1966) MR 35:1007

12.
C.T.C. Wall, Poincaré complexes I, Annals of Math. 86 (1967), 213-245 MR 36:880

13.
-, Surgery on compact manifolds, Academic Press London & New York (1970) MR 55:4217

14.
G.W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, Springer-Verlag, New York (1978) MR 80b:55001

15.
H. Whitney, The singularities of a smooth $n$-manifold in $(2n-1)$-space, Annals of Math. 45 (1944) 247-293 MR 5:274a


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Additional Information:

Yanghyun Byun
Affiliation: Department of Mathematics, Hanyang University, Seongdong-Gu, Seoul, Korea
Email: yhbyun@fermat.hanyang.ac.kr

DOI: 10.1090/S0002-9947-98-02274-0
PII: S 0002-9947(98)02274-0
Received by editor(s): July 29, 1996
Additional Notes: Partially supported by 1996 Faculty Research Fund of Hanyang University, Korea.
Copyright of article: Copyright 1998, American Mathematical Society


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