×

zbMATH — the first resource for mathematics

Extending monotone decompositions of 3-manifolds. (English) Zbl 0205.53401

MSC:
57N10 Topology of general \(3\)-manifolds (MSC2010)
57N12 Topology of the Euclidean \(3\)-space and the \(3\)-sphere (MSC2010)
54B15 Quotient spaces, decompositions in general topology
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] R. H. Bing, A characterization of 3-space by partitionings, Trans. Amer. Math. Soc. 70 (1951), 15 – 27. · Zbl 0042.41903
[2] R. H. Bing, Concerning hereditarily indecomposable continua, Pacific J. Math. 1 (1951), 43 – 51. · Zbl 0043.16803
[3] R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145 – 158. · Zbl 0055.16802 · doi:10.2307/1969836 · doi.org
[4] R. H. Bing, An alternative proof that 3-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37 – 65. · Zbl 0106.16604 · doi:10.2307/1970092 · doi.org
[5] -, “Decompositions of \( {E^3}\)” in Topology of 3-manifolds and related topics (Proc. Univ. of Georgia Institute, 1961), Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 5-21. MR 25 #4501.
[6] B. G. Casler, An imbedding theorem for connected 3-manifolds with boundary, Proc. Amer. Math. Soc. 16 (1965), 559 – 566. · Zbl 0129.15801
[7] J. F. P. Hudson and E. C. Zeeman, On regular neighbourhoods, Proc. London Math. Soc. (3) 14 (1964), 719 – 745. · Zbl 0123.39601 · doi:10.1112/plms/s3-14.4.719 · doi.org
[8] Edwin E. Moise, Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96 – 114. · Zbl 0048.17102 · doi:10.2307/1969769 · doi.org
[9] 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. · Zbl 0055.16804 · doi:10.2307/1969837 · doi.org
[10] J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. (2), 45 (1939), 243-327. · Zbl 0022.40702
[11] G. T. Whyburn, Decomposition spaces, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 2 – 4. · Zbl 1246.57004
[12] E. C. Zeeman, Polyhedral \?-manifolds. II. Embeddings, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 65 – 70. · Zbl 1246.57064
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.