Finite-dimensional complement theorems: examples and results
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- by R. B. Sher and G. A. Venema PDF
- Proc. Amer. Math. Soc. 103 (1988), 299-306 Request permission
Abstract:
Examples are given which show the necessity of various hypotheses in the known finite dimensional complement theorems. In addition, several positive results are presented which improve one direction of such theorems.References
- T. A. Chapman, On some applications of infinite-dimensional manifolds to the theory of shape, Fund. Math. 76 (1972), no. 3, 181–193. MR 320997, DOI 10.4064/fm-76-3-181-193
- T. A. Chapman, Shapes of finite-dimensional compacta, Fund. Math. 76 (1972), no. 3, 261–276. MR 320998, DOI 10.4064/fm-76-3-261-276
- Eldon Dyer and A. T. Vasquez, The sphericity of higher dimensional knots, Canadian J. Math. 25 (1973), 1132–1136. MR 326708, DOI 10.4153/CJM-1973-121-5
- Michael H. Freedman, The disk theorem for four-dimensional manifolds, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 647–663. MR 804721
- L. S. Husch and I. Ivanšić, Embedding compacta up to shape, Shape theory and geometric topology (Dubrovnik, 1981) Lecture Notes in Math., vol. 870, Springer, Berlin-New York, 1981, pp. 119–134. MR 643527
- L. S. Husch and I. Ivanšić, On shape concordances, Shape theory and geometric topology (Dubrovnik, 1981) Lecture Notes in Math., vol. 870, Springer, Berlin-New York, 1981, pp. 135–149. MR 643528
- L. S. Husch and I. Ivanšić, Shape domination and embedding up to shape, Compositio Math. 40 (1980), no. 2, 153–166. MR 563539
- I. Ivanšić, R. B. Sher, and G. A. Venema, Complement theorems beyond the trivial range, Illinois J. Math. 25 (1981), no. 2, 209–220. MR 607023, DOI 10.1215/ijm/1256047254
- J. Levine, Unknotting spheres in codimension two, Topology 4 (1965), 9–16. MR 179803, DOI 10.1016/0040-9383(65)90045-5
- Vo Thanh Liem and Gerard A. Venema, Stable shape concordance implies homeomorphic complements, Fund. Math. 126 (1986), no. 2, 123–131. MR 843241, DOI 10.4064/fm-126-2-123-131
- Sibe Mardešić and Jack Segal, Shape theory, North-Holland Mathematical Library, vol. 26, North-Holland Publishing Co., Amsterdam-New York, 1982. The inverse system approach. MR 676973
- Sławomir Nowak, On the relationships between shape properties of subcompacta of $S^n$ and homotopy properties of their complements, Fund. Math. 128 (1987), no. 1, 47–60. MR 919289, DOI 10.4064/fm-128-1-47-59
- R. B. Sher, Complement theorems in shape theory, Shape theory and geometric topology (Dubrovnik, 1981) Lecture Notes in Math., vol. 870, Springer, Berlin-New York, 1981, pp. 150–168. MR 643529
- R. B. Sher, Complement theorems in shape theory. II, Geometric topology and shape theory (Dubrovnik, 1986) Lecture Notes in Math., vol. 1283, Springer, Berlin, 1987, pp. 212–220. MR 922283, DOI 10.1007/BFb0081430
- R. B. Sher, A complement theorem for shape concordant compacta, Proc. Amer. Math. Soc. 91 (1984), no. 1, 123–132. MR 735578, DOI 10.1090/S0002-9939-1984-0735578-2
- D. W. Sumners, Homotopy torsion in codimension two knots, Proc. Amer. Math. Soc. 24 (1970), 229–240. MR 253316, DOI 10.1090/S0002-9939-1970-0253316-7 J. Stallings, The embedding of homotopy types into manifolds, mimeographed notes, Princeton University.
- John Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481–488. MR 149457, DOI 10.1017/S0305004100036756
- Gerard A. Venema, Embeddings of compacta with shape dimension in the trivial range, Proc. Amer. Math. Soc. 55 (1976), no. 2, 443–448. MR 397738, DOI 10.1090/S0002-9939-1976-0397738-8
- Gerard A. Venema, Neighborhoods of compacta in Euclidean space, Fund. Math. 109 (1980), no. 1, 71–78. MR 594326, DOI 10.4064/fm-109-1-71-78
- J. H. C. Whitehead, Combinatorial homotopy. I, Bull. Amer. Math. Soc. 55 (1949), 213–245. MR 30759, DOI 10.1090/S0002-9904-1949-09175-9
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 299-306
- MSC: Primary 57N25; Secondary 54C56
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938687-1
- MathSciNet review: 938687