Taming embeddings of certain polyhedra in codimension three
HTML articles powered by AMS MathViewer
- by T. B. Rushing PDF
- Trans. Amer. Math. Soc. 145 (1969), 87-103 Request permission
References
-
H. W. Berkowitz, Counterexample to a theorem of T. Homma, Abstract 68T-264, Notices Amer. Math. Soc. 15 (1968), 378.
- R. H. Bing and J. M. Kister, Taming complexes in hyperplanes, Duke Math. J. 31 (1964), 491–511. MR 164329
- John L. Bryant, Taming polyhedra in the trivial range, Michigan Math. J. 13 (1966), 377–384. MR 206967 J. L. Bryant and C. L. Seebeck III, Locally nice embeddings of polyhedra, Quart. J. Math. Oxford Ser. (to appear).
- J. L. Bryant and C. L. Seebeck III, Locally nice embeddings in codimension three, Bull. Amer. Math. Soc. 74 (1968), 378–380. MR 221514, DOI 10.1090/S0002-9904-1968-11960-3
- J. C. Cantrell, $n$-frames in euclidean $k$-space, Proc. Amer. Math. Soc. 15 (1964), 574–578. MR 164330, DOI 10.1090/S0002-9939-1964-0164330-1 J. C. Cantrell and R. C. Lacher, Some conditions for manifolds to be locally flat, (mimeographed).
- J. C. Cantrell and R. C. Lacher, Local flattening of a submanifold, Quart. J. Math. Oxford Ser. (2) 20 (1969), 1–10. MR 239598, DOI 10.1093/qmath/20.1.1 A. V. Černavskiĭ, Homeomorphisms of euclidean space and topological embeddings of polyhedra in euclidean space, Mat. Sb. 63 (1965), 581-613.
- A. V. Černavskiĭ, Homeomorphisms of euclidean space and topological imbeddings of polyhedra into euclidean spaces. II, Mat. Sb. (N.S.) 72 (114) (1967), 573–601 (Russian). MR 0208582
- A. V. Černavskiĭ, On singular points of topological imbeddings of manifolds and the union of locally flat cells, Dokl. Akad. Nauk SSSR 167 (1966), 528–530 (Russian). MR 0198447
- Marshall M. Cohen, A general theory of relative regular neighborhoods, Trans. Amer. Math. Soc. 136 (1969), 189–229. MR 248802, DOI 10.1090/S0002-9947-1969-0248802-6
- Richard H. Crowell and Ralph H. Fox, Introduction to knot theory, Ginn and Company, Boston, Mass., 1963. Based upon lectures given at Haverford College under the Philips Lecture Program. MR 0146828
- Jerome Dancis, Some nice embeddings in the trivial range, Topology Seminar (Wisconsin, 1965) Ann. of Math. Studies, No. 60, Princeton Univ. Press, Princeton, N.J., 1966, pp. 159–170. MR 0220265 P. F. Duvall, Jr., Neighborhoods of 1-connected ANR’s in high dimensional piecewise linear manifolds, Ph.D. Dissertation, University of Georgia, Athens, Georgia, 1967.
- Samuel Eilenberg and R. L. Wilder, Uniform local connectedness and contractibility, Amer. J. Math. 64 (1942), 613–622. MR 7100, DOI 10.2307/2371708
- L. C. Glaser and T. M. Price, Unknotting locally flat cell pairs, Illinois J. Math. 10 (1966), 425–430. MR 196735, DOI 10.1215/ijm/1256054995
- Charles Greathouse, Locally flat, locally tame, and tame embeddings, Bull. Amer. Math. Soc. 69 (1963), 820–823. MR 155306, DOI 10.1090/S0002-9904-1963-11050-2
- Herman Gluck, Embeddings in the trivial range, Ann. of Math. (2) 81 (1965), 195–210. MR 173243, DOI 10.2307/1970614
- Herman Gluck, Restriction of isotopies, Bull. Amer. Math. Soc. 69 (1963), 78–82. MR 143190, DOI 10.1090/S0002-9904-1963-10867-8
- Charles Greathouse, Locally flat, locally tame, and tame embeddings, Bull. Amer. Math. Soc. 69 (1963), 820–823. MR 155306, DOI 10.1090/S0002-9904-1963-11050-2
- J. P. Hempel and D. R. McMillan Jr., Locally nice embeddings of manifolds, Amer. J. Math. 88 (1966), 1–19. MR 205257, DOI 10.2307/2373043 T. Homma, Piecewise linear approximations of embeddings of manifolds, Mimeographed notes, The Florida State Univ., Tallahassee, 1965.
- Tatsuo Homma, On the imbedding of polyhedra in manifolds, Yokohama Math. J. 10 (1962), 5–10. MR 154287
- Tatsuo Homma, A theorem of piecewise linear approximations, Yokohama Math. J. 14 (1966), 47–54. MR 217803
- J. F. P. Hudson, Piecewise linear embeddings and isotopies, Bull. Amer. Math. Soc. 72 (1966), 536–537. MR 193642, DOI 10.1090/S0002-9904-1966-11532-X
- J. F. P. Hudson, Concordance and isotopy of $\textrm {PL}$ embeddings, Bull. Amer. Math. Soc. 72 (1966), 534–535. MR 193641, DOI 10.1090/S0002-9904-1966-11530-6
- J. F. P. Hudson and E. C. Zeeman, On regular neighbourhoods, Proc. London Math. Soc. (3) 14 (1964), 719–745. MR 166790, DOI 10.1112/plms/s3-14.4.719
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- Lawrence S. Husch, On relative regular neighbourhoods, Proc. London Math. Soc. (3) 19 (1969), 577–585. MR 250315, DOI 10.1112/plms/s3-19.4.577
- M. C. Irwin, Embeddings of polyhedral manifolds, Ann. of Math. (2) 82 (1965), 1–14. MR 182978, DOI 10.2307/1970560
- C. Lacher, Locally flat strings and half-strings, Proc. Amer. Math. Soc. 18 (1967), 299–304. MR 212805, DOI 10.1090/S0002-9939-1967-0212805-1
- W. B. R. Lickorish, The piecewise linear unknotting of cones, Topology 4 (1965), 67–91. MR 203736, DOI 10.1016/0040-9383(65)90049-2
- R. Penrose, J. H. C. Whitehead, and E. C. Zeeman, Imbedding of manifolds in euclidean space, Ann. of Math. (2) 73 (1961), 613–623. MR 124909, DOI 10.2307/1970320 T. B. Rushing, Unknotting locally flat embeddings by isotopy, Abstract 656-78, Notices Amer. Math. Soc. 15 (1968), 525.
- Charles Seebeck, $\varepsilon$-taming in codimension $3$, Michigan Math. J. 14 (1967), 89–93. MR 208584
- John Stallings, On topologically unknotted spheres, Ann. of Math. (2) 77 (1963), 490–503. MR 149458, DOI 10.2307/1970127 R. Tindell, The knotting set of a piecewise linear imbedding, mimeographed.
- C. Weber, Plongements de polyhèdres dans le domaine métastable, Comment. Math. Helv. 42 (1967), 1–27 (French). MR 238330, DOI 10.1007/BF02564408
- E. C. Zeeman, Unknotting combinatorial balls, Ann. of Math. (2) 78 (1963), 501–526. MR 160218, DOI 10.2307/1970538 —, “Polyhedral manifolds, II. Embeddings” in Topology of 3-manifolds, Prentice-Hall, Englewood Cliffs, N. J., 1962. —, Seminar on combinatorial topology, Mimeographed, Inst. Hautes Etudes Sci., Paris, 1963.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 145 (1969), 87-103
- MSC: Primary 57.01
- DOI: https://doi.org/10.1090/S0002-9947-1969-0250316-4
- MathSciNet review: 0250316