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Stable thickenings in the topological category


Author: R. L. Chazin
Journal: Proc. Amer. Math. Soc. 29 (1971), 175-178
MSC: Primary 57A55
DOI: https://doi.org/10.1090/S0002-9939-1971-0296950-1
MathSciNet review: 0296950
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Abstract: A thickening, in the topological category, of a complex K is an equivalence class of simple homotopy equivalences $ \phi :K \to M$, where M is a topological manifold with boundary. Here it is shown that for stable thickenings ( $ \dim M \gg \dim K$), the set $ \Im (K)$ of stable thickenings is in 1-1 correspondence with homotopy classes of maps of K into BTop.


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  • [1] C. T. C. Wall, Classification problems in differential topology. IV, Topology 5 (1966), 73-94. MR 33 #734. MR 0192509 (33:734)
  • [2] B. Mazur, Differential topology from the point of view of simple homotopy theory, Inst. Hautes Études Sci. Publ. Math. No. 15 (1963). MR 28 #4550. MR 0161342 (28:4550)
  • [3] 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)
  • [4] J. A. Lees, Immersions and surgeries of topological manifolds, Bull. Amer. Math. Soc. 75 (1969), 529-534. MR 39 #959. MR 0239602 (39:959)
  • [5] D. Gauld, Mersions of topological manifolds, Thesis, University of California, Los Angeles, Calif., 1969. MR 0266217 (42:1124)
  • [6] J. Dancis, Approximations and isotopies in the trivial range, Topology Seminar (Wisconsin, 1965), Ann. of Math. Studies, no. 60, Princeton Univ. Press, Princeton, N. J., 1966. MR 36 #7144. MR 0224097 (36:7144)
  • [7] J. A. Lees, Thesis, Rice University, Houston, Tex., 1968.
  • [8] M. H. A. Newman, The engulfing theorem for topological manifolds, Ann. of Math. (2) 84 (1966), 555-571. MR 34 #3557. MR 0203708 (34:3557)
  • [9] E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966. MR 35 #1007. MR 0210112 (35:1007)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0296950-1
Keywords: Thickening, stable thickening, topological manifold, classification of stable thickenings
Article copyright: © Copyright 1971 American Mathematical Society

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