Embedding phenomena based upon decomposition theory: an unusual cellular -cell

Author:
Robert J. Daverman

Journal:
Proc. Amer. Math. Soc. **75** (1979), 183-185

MSC:
Primary 57N60; Secondary 57N10, 57N15

MathSciNet review:
529238

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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a 2-cell *D* cellularly embedded in the *n*-sphere , and locally flatly embedded at each of its interior points, but the boundary of which fails to be weakly flat.

**[1]**J. W. Cannon,*Shrinking cell-like decompositions of manifolds. Codimension three*, Ann. of Math. (2)**110**(1979), no. 1, 83–112. MR**541330**, 10.2307/1971245**[2]**Robert J. Daverman,*On weakly flat 1-spheres*, Proc. Amer. Math. Soc.**38**(1973), 207–210. MR**0310894**, 10.1090/S0002-9939-1973-0310894-X**[3]**R. J. Daverman and T. B. Rushing,*Weak flatness criteria for codimension 2 spheres in codimension 1 manifolds*, General Topology and Appl.**6**(1976), no. 1, 101–115. MR**0394681****[4]**Paul F. Duvall Jr.,*Weakly flat spheres*, Michigan Math. J.**16**(1969), 117–124. MR**0246300****[5]**R. D. Edwards,*Suspensions of homology spheres*(to appear).**[6]**-,*Approximating certain cell-like maps by homeomorphisms*(to appear).**[7]**J. G. Hollingsworth and T. B. Rushing,*Homotopy characterizations of weakly flat codimension 2 spheres*, Amer. J. Math.**98**(1976), no. 2, 385–394. MR**0420631****[8]**Barry Mazur,*A note on some contractible 4-manifolds*, Ann. of Math. (2)**73**(1961), 221–228. MR**0125574****[9]**D. R. McMillan Jr.,*A criterion for cellularity in a manifold*, Ann. of Math. (2)**79**(1964), 327–337. MR**0161320****[10]**M. H. A. Newman,*The engulfing theorem for topological manifolds*, Ann. of Math. (2)**84**(1966), 555–571. MR**0203708**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1979-0529238-9

Keywords:
Weakly flat sphere,
cellular cell,
globally 1-alg,
cellularity criterion,
homology sphere,
double suspension,
mapping torus

Article copyright:
© Copyright 1979
American Mathematical Society