On replacing proper Dehn maps with proper embeddings
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- by C. D. Feustel
- Trans. Amer. Math. Soc. 166 (1972), 261-267
- DOI: https://doi.org/10.1090/S0002-9947-1972-0293644-9
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Abstract:
In this paper we develop algebraic and geometric conditions which imply that a given proper Dehn map can be replaced by an embedding. The embedding, whose existence is implied by our theorem, retains most of the algebraic and geometric properties required in the original proper Dehn map.References
- E. M. Brown, Unknotting in $M^{2}\times I$, Trans. Amer. Math. Soc. 123 (1966), 480–505. MR 198482, DOI 10.1090/S0002-9947-1966-0198482-0
- Wolfgang Heil, On $P^{2}$-irreducible $3$-manifolds, Bull. Amer. Math. Soc. 75 (1969), 772–775. MR 251731, DOI 10.1090/S0002-9904-1969-12283-4
- C. D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1–26. MR 90053, DOI 10.2307/1970113
- John Stallings, On the loop theorem, Ann. of Math. (2) 72 (1960), 12–19. MR 121796, DOI 10.2307/1970146
- J. H. C. Whitehead, The mathematical works of J. H. C. Whitehead. Vol. I: Differential geometry, Pergamon Press, Oxford-New York-Paris, 1962. Edited by I.M. James. With a biographical note by M. H. A. Newman and Barbara Whitehead and a mathematical appreciation by John W. Milnor. MR 0174463
- Friedhelm Waldhausen, Gruppen mit Zentrum und $3$-dimensionale Mannigfaltigkeiten, Topology 6 (1967), 505–517 (German). MR 236930, DOI 10.1016/0040-9383(67)90008-0
- Friedhelm Waldhausen, On irreducible $3$-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56–88. MR 224099, DOI 10.2307/1970594
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 166 (1972), 261-267
- MSC: Primary 57D40
- DOI: https://doi.org/10.1090/S0002-9947-1972-0293644-9
- MathSciNet review: 0293644