The Hauptvermutung for $3$-complexes
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- by Edward M. Brown PDF
- Trans. Amer. Math. Soc. 144 (1969), 173-196 Request permission
References
- R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145–158. MR 61377, DOI 10.2307/1969836 E. M. Brown, The Hauptvermutung for 3-complexes, Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1963.
- 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
- Stewart S. Cairns, The triangulation problem and its role in analysis, Bull. Amer. Math. Soc. 52 (1946), 545–571. MR 17531, DOI 10.1090/S0002-9904-1946-08610-3
- Herman Gluck, The weak Hauptvermutung for cells and spheres, Bull. Amer. Math. Soc. 66 (1960), 282–284. MR 117730, DOI 10.1090/S0002-9904-1960-10472-7
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- J. M. Kister, Isotopies in $3$-manifolds, Trans. Amer. Math. Soc. 97 (1960), 213–224. MR 120628, DOI 10.1090/S0002-9947-1960-0120628-5
- John Milnor, Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math. (2) 74 (1961), 575–590. MR 133127, DOI 10.2307/1970299
- Edwin E. Moise, Affine structures in $3$-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96–114. MR 48805, DOI 10.2307/1969769
- Edwin E. Moise, Affine structures in $3$-manifolds. VIII. Invariance of the knot-types; local tame imbedding, Ann. of Math. (2) 59 (1954), 159–170. MR 61822, DOI 10.2307/1969837
- James Munkres, The triangulation of locally triangulable spaces, Acta Math. 97 (1957), 67–93. MR 87926, DOI 10.1007/BF02392393
- Ch. Papakyriakopoulos, A new proof for the invariance of the homology groups of a complex, Bull. Soc. Math. Grèce 22 (1943), 1–154 (1946) (Greek). MR 24619 H. Poincaré, Sur l’analysis situs, C. R. Acad. Sci. Paris, 115 (1892), 463-636. —, Complement a l’analysis situs, Rend. Circ. Mat. Palermo 13 (1899), 285-343.
- Stephen Smale, Differentiable and combinatorial structures on manifolds, Ann. of Math. (2) 74 (1961), 498–502. MR 133133, DOI 10.2307/1970294 E. Steinitz, Beiträge zur Analysis situs, S.-B. Berlin. Math. Ges. 7 (1908), 29-49.
- Heinrich Tietze, Über die topologischen Invarianten mehrdimensionaler Mannigfaltigkeiten, Monatsh. Math. Phys. 19 (1908), no. 1, 1–118 (German). MR 1547755, DOI 10.1007/BF01736688 J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. (2) 45 (1939), 243-327. E. C. Zeeman, Seminar on combinatorial topology, (mimeographed), Inst. Hautes Études Sci., Paris, 1963.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 144 (1969), 173-196
- MSC: Primary 57.01; Secondary 54.00
- DOI: https://doi.org/10.1090/S0002-9947-1969-0251729-7
- MathSciNet review: 0251729