# zbMATH — the first resource for mathematics

A method for shrinking decompositions of certain manifolds. (English) Zbl 0244.57004

##### MSC:
 57N15 Topology of the Euclidean $$n$$-space, $$n$$-manifolds ($$4 \leq n \leq \infty$$) (MSC2010) 57N99 Topological manifolds 54B15 Quotient spaces, decompositions in general topology 57M40 Characterizations of the Euclidean $$3$$-space and the $$3$$-sphere (MSC2010)
Full Text:
##### References:
 [1] J. J. Andrews and M. L. Curtis, \?-space modulo an arc, Ann. of Math. (2) 75 (1962), 1 – 7. · Zbl 0105.17403 [2] R. H. Bing, The cartesian product of a certain nonmanifold and a line is \?$$^{4}$$, Ann. of Math. (2) 70 (1959), 399 – 412. · Zbl 0089.39501 [3] -, Decompositions of $${E^3}$$, Topology of 3-Manifolds and Related Topics (Proc. Univ. of Georgia Inst., 1961), Prentice-Hall, Englewood Cliffs, N. J., 1962, pp. 5-21. MR 25 #4501. [4] R. H. Bing, Radial engulfing, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967) Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 1 – 18. [5] J. L. Bryant, Euclidean n-space modulo an $$(n - 1)$$-cell (to appear). · Zbl 0262.57002 [6] E. H. Connell, A topological \?-cobordism theorem for \?\ge 5, Illinois J. Math. 11 (1967), 300 – 309. · Zbl 0146.45201 [7] James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. · Zbl 0144.21501 [8] Leslie C. Glaser, On the double suspension of certain homotopy 3-spheres, Ann. of Math. (2) 85 (1967), 494 – 507. · Zbl 0171.44301 [9] Leslie C. Glaser, On suspensions of homology spheres, Manifolds – Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Mathematics, Vol. 197, Springer, Berlin, 1971, pp. 8 – 16. [10] Leslie C. Glaser, A decomposition proof that the double suspension of a homotopy 3-cell is a topological 5-cell, Illinois J. Math. 16 (1972), 475 – 490. · Zbl 0238.57004 [11] L. C. Glaser and J. Hollingsworth, Geometrical techniques for studying simplicial triangulations of topological manifolds (to appear). [12] Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. · Zbl 0029.32203 [13] R. C. Kirby and L. C. Siebenmann, For manifolds the Hauptvermutung and the triangulation conjecture are false, Notices Amer. Math. Soc. 16 (1969), 695. Abstract #69T-G80. · Zbl 0189.54701 [14] C. Lacher, Some conditions for manifolds to be locally flat, Trans. Amer. Math. Soc. 126 (1967), 119 – 130. · Zbl 0161.42604 [15] Louis F. McAuley, Some upper semi-continuous decompositions of \?³ into \?³, Ann. of Math. (2) 73 (1961), 437 – 457. · Zbl 0098.14403 [16] -, Upper semicontinuous decompositions of $${E^3}$$ into $${E^3}$$ and generalizations to metric spaces, Topology of 3-Manifolds and Related Topics (Proc. Univ. of Georgia Inst., 1961), Prentice-Hall, Englewood Cliffs, N. J., 1962, pp. 21-26. MR 25 #4502. · Zbl 1246.57051 [17] Ernest Michael, Local properties of topological spaces, Duke Math. J. 21 (1954), 163 – 171. · Zbl 0055.16203 [18] Ronald H. Rosen, Concerning suspension spheres, Proc. Amer. Math. Soc. 23 (1969), 225 – 231. · Zbl 0184.48602 [19] L. C. Siebenmann, On detecting Euclidean space homotopically among topological manifolds., Invent. Math. 6 (1968), 245 – 261. · Zbl 0169.55201 [20] -, A renontriangulable manifolds triangulable ?, Proc. Georgia Conference, 1969, Topology of Manifolds, Markham, Chicago, 1969, pp. 77-84. [21] L. C. Siebenmann, Approximating cellular maps by homeomorphisms, Topology 11 (1972), 271 – 294. · Zbl 0216.20101 [22] John Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481 – 488. · Zbl 0107.40203 [23] A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690 – 700. · Zbl 0071.16001 [24] Perrin Wright, Radial engulfing in codimension three, Duke Math. J. 38 (1971), 295 – 298. · Zbl 0217.20102 [25] William L. Voxman, On the shrinkability of decompositions of 3-manifolds, Trans. Amer. Math. Soc. 150 (1970), 27 – 39. · Zbl 0198.56304
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.