Pacific Journal of Mathematics

Compact contractible $n$-manifolds have arc spines $(n\geq 5)$.

Fredric D. Ancel and Craig R. Guilbault

Article information

Source
Pacific J. Math., Volume 168, Number 1 (1995), 1-10.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102620675

Mathematical Reviews number (MathSciNet)
MR1331991

Zentralblatt MATH identifier
0820.57014

Subjects
Primary: 57Q15: Triangulating manifolds
Secondary: 54C99: None of the above, but in this section 57N15: Topology of $E^n$ , $n$-manifolds ($4 \less n \less \infty$) 57N45: Flatness and tameness

Citation

Ancel, Fredric D.; Guilbault, Craig R. Compact contractible $n$-manifolds have arc spines $(n\geq 5)$. Pacific J. Math. 168 (1995), no. 1, 1--10. https://projecteuclid.org/euclid.pjm/1102620675


Export citation

References

  • [1] J. L. Bryant and R. C. Lacher, Mapping cylinder neighborhoods on one- complexes in four-space, Trans. Amer. Math. Soc. 164 (1972), 333-339.
  • [2] E. H. Connell, A topological h-cobordism theorem, Illinois J. Math., 11 (1967), 300-309.
  • [3] R. J. Daverman and F. C. Tinsley, Laminations, finitely generated perfect groups, and acyclic maps, Michigan Math. J., 33 (1986), 343-351.
  • [4] R. J. Daverman and F. C. Tinsley, Acyclic maps whose mapping cylinders embed in ^-manifolds, Houston J. of Math, 16 (1990), 255-270.
  • [5] J. Dugundji, Topology, Allyn and Bacon, 1966.
  • [6] R. D. Edwards, The topology of manifolds and cell-like maps, Proc. Inter- nat. Congress of Mathematicians, Helsinki, 1978 (Lethi, O., ed.) Acad. Sci. Fenn. 1980, Helsinki, 111-127.
  • [7] M. H. Freedman, The topology of four-dimensional manifolds, J. Differ- ential Geom., 17 (1982), 357-453.
  • [8] J. C. Hausmann, Homological surgery, Annals of Math., 104 (1976), 573- 584.
  • [9] S. T. Hu, Homotopy Theory, Academic Press, 1959.
  • [10] S. T. Hu, Theory of Retracts, Wayne State University Press, 1965.
  • [11] M. A. Kervaire, Smooth homology spheres and their fundamental groups, Trans. Amer. Math. Soc, 144 (1969), 67-72.
  • [12] R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc, 75 (1969), 742-749.
  • [13] R. Lashof and M. Rothenberg, Microbundles and smoothing, Topology, 3 (1964), 357-388.
  • [14] W. B. R. Lickorish and L. C. Siebenmann, Regular neighborhoods and the stable range, Trans. Amer. Math. Soc, 139 (1969), 207-230.
  • [15] M. H. A. Newman, Boundaries of ULC sets in Euclidean n-space, Proc Natl. Acad. Sci., USA 34 (1948), 193-196.
  • [16] V. Nicholson, Mapping cylinder neighborhoods, Trans. Amer.Math. Soc, 143 (1969), 259-268.
  • [17] D. G. Wright, Sticky arcs in En(n > 4), Proc Amer. Math. Soc, 66 (1977), 181-182.