Inventiones mathematicae

, Volume 78, Issue 2, pp 161–222

An extension of the Loop theorem and resolutions of generalized 3-manifolds with 0-dimensional singular set

  • T. L. Thickstun


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B] Borsuk, K.: Theory of retracts. Monogr. Mat., Tom 44. PWN, Warszawa 1967Google Scholar
  2. [Br] Brin, M.G.: Torsion free actions on 1-acyclic manifolds and the loop theorem. Topology20, 353–363 (1981)Google Scholar
  3. [B-B-F] Brown, E.M., Brown, M.S., Feustel, C.D.: On properly embedding planes in 3-manifolds. Proc. Amer. Math. Soc.55, 461–464 (1976)Google Scholar
  4. [B-M] Brin, M.G., McMillan, D.R., Jr.: Generalized 3-manifolds with zero-dimensional singular set. Pac J. Math.97, 29–58 (1981)Google Scholar
  5. [C] Cannon, J.W.: The recognition problem: What is a topological manifold? BAMS 84, 832–866 (1978)Google Scholar
  6. [C-B-L] Cannon, J.W., Bryant, J.L., Lacher, R.C.: The structure of generalized manifolds having non-manifold set of trivial dimension. In: Geometric Topology Cantrell, J.C., (ed.), pp. 261–263. New York: Academic Press 1979Google Scholar
  7. [C-G] Casson, A.J., Gordon, C.McA.: A loop theorem for duality spaces and fibered ribbon knots. Invent. Math.74, 119–137 (1983)Google Scholar
  8. [E] Edwards, C.H., Jr.: Open 3-manifolds which are simply connected at ∞. Proc. Amer. Math. Soc.14, 391–395 (1963)Google Scholar
  9. [F] Freudenthal, H.: Neuaufbau der Endentheorie. Ann. of Math. (1942)Google Scholar
  10. [H] Henderson, D.W.: Extensions of Dehn's lemma and the loop theorem. Trans. AMS120, 448–469 (1965)Google Scholar
  11. [He] Hempel, J.: 3-Manifolds. Annals of Mathematics Studies. Princeton: University Press 1976Google Scholar
  12. [H-S] Hass, J., Scott, G.P.: Intersections of curves on surfaces. PreprintGoogle Scholar
  13. [L1] Lacher, R.C.: Cell-like mappings I. Pae. J. Math.30, 717–731 (1969)Google Scholar
  14. [L2] Lacher, R.C.: Cell-like mappings and their generalizations. BAMS83, 495–552 (1977)Google Scholar
  15. [L3] Lacher, R.C.: Generalized three-manifolds. In: Shape Theory and Geometric Topology (Proceedings, Dubrovnik 1981). Lecture Notes in Mathematics, vol. 870. Berlin-Heidelberg-New York: Springer 1981Google Scholar
  16. [M] Maskit, B.: A theorem on planar covering, surfaces with applications to 3-manifolds. Ann. of Math.81, 341–355 (1965)Google Scholar
  17. [P] Papakyriakopoulos, C.D.: On solid tori. Proc. London Math. Soc.7, 281–299 (1957)Google Scholar
  18. [Q1] Quinn, F.: Resolutions of homology manifolds and the topological characterization of manifolds. Invent. Math.72, 267–284 (1983)Google Scholar
  19. [Q2] Quinn, F.: Ends of maps III. Dimensions 4 and 5. J. Differential Geom.17, (No. 3) 503–521 (1982)Google Scholar
  20. [Sp] Spanier, E.H.: Algebraic topology. New York: McGraw Hill 1966Google Scholar
  21. [St] Stallings, J.R.: On the loop theorem. Ann. of Math.72, 12–19 (1960)Google Scholar
  22. [T1] Thickstun, T.L.: Open acyclic 3-manifolds, a loop theorem and the Poincaré conjecture. PreprintGoogle Scholar
  23. [T2] Thickstun, T.L.: Open acyclic 3-manifolds, a loop theorem and the Poincaré conjecture. BAMS (New Series), Vol. 4, Number 2, 192–194 (1981)Google Scholar
  24. [W] Wall, C.T.C.: Open 3-manifolds which are 1-connected at infinity. J. Math. Oxford16(2) 263–268 (1965)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • T. L. Thickstun
    • 1
    • 2
  1. 1.University College of North WalesBangor, WalesUK
  2. 2.Department of MathematicsSouthwest Texas State UniversitySan MarcosUSA

Personalised recommendations