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Regular neighborhoods and topological manifolds


Author: Glenn P. Weller
Journal: Proc. Amer. Math. Soc. 42 (1974), 320-325
MSC: Primary 57A40
DOI: https://doi.org/10.1090/S0002-9939-1974-0328949-3
MathSciNet review: 0328949
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Abstract: This paper defines a notion of topological regular neighborhood for compact triangulable subspaces of topological manifolds, proves a uniqueness theorem for such neighborhoods, and shows that this theorem is in a sense the best possible. These results have obvious applications to regular neighborhoods in manifolds having more than one piecewise linear structure.


References [Enhancements On Off] (What's this?)

  • [1] M. A. Armstrong, Collars and concordances of topological manifolds, Comment. Math. Helv. 45 (1970), 119-128. MR 42 #1128. MR 0266221 (42:1128)
  • [2] T. Chapman, The topological invariance of Whitehead torsion, Amer. J. Math. (to appear). MR 0391109 (52:11931)
  • [3] M. M. Cohen, A course in simple-homotopy theory, Graduate Texts in Math. 10, Springer-Verlag, New York (to appear). MR 0362320 (50:14762)
  • [4] J. F. P. Hudson, Piecewise linear topology, Univ. of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees, Benjamin, New York, 1969. MR 40 #2094. MR 0248844 (40:2094)
  • [5] M. Kato, Regular neighborhoods are not topologically invariant, Bull. Amer. Math. Soc. 74 (1968), 988-991. MR 37 #4804. MR 0229230 (37:4804)
  • [6] R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742-749. MR 39 #3500. MR 0242166 (39:3500)
  • [7] -, Some theorems on topological manifolds, Manifolds--Amsterdam, 1970 (Proc. Nuffic Summer School), Lecture Notes in Math., vol. 197, Springer, Berlin, 1971, pp. 1-7. MR 44 #1037. MR 0283807 (44:1037)
  • [8] K. W. Kwun, Uniqueness of the open cone neighborhood, Proc. Amer. Math. Soc. 15 (1964) 476-479. MR 28 #4527. MR 0161319 (28:4527)
  • [9] K. W. Kwun and F. Raymond, Mapping cylinder neighborhoods, Michigan Math. J. 10 (1963), 353-357. MR 27 #6248. MR 0156324 (27:6248)
  • [10] R. T. Miller, Close isotopies on piecewise linear manifolds, Trans. Amer. Math. Soc. 151 (1970), 597-628. MR 42 #1127. MR 0266220 (42:1127)
  • [11] J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966), 358-426. MR 33 #4922. MR 0196736 (33:4922)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328949-3
Keywords: Topological manifold, piecewise linear manifold, regular neighborhood, triangulation, Hauptvermutung, Whitehead torsion, mapping cylinder neighborhood, open cone neighborhood
Article copyright: © Copyright 1974 American Mathematical Society

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