Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T13:17:59.008Z Has data issue: false hasContentIssue false
  • English
  • Français

On Kneser's conjecture for bounded 3-manifolds

Published online by Cambridge University Press:  24 October 2008

Wolfgang Heil
Wolfgang Heil
Affiliation:
The Florida State University, Tallahassee, Florida 32306, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

1. The classical Kneser conjecture states that if M is a closed 3-manifold and π1(M) ≈ A * B, a free product, then there exist 3-manifolds MA, MB such that

and π1(MA) ≈ A, π1(MB) ≈ B. This has been proved by John Stallings(6).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 243 - 246
Copyright
Copyright © Cambridge Philosophical Society 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Haken, W.Ein Verfahren zur Aufspaltung einer 3-Mannigfaltigkeit in irreduzible 3-Mannig. faltigkeiten. Math. Z. 76 (1961), 427–467.CrossRefGoogle Scholar
(2)Hempel, J.Kneser's conjecture, mimeographed lecture notes. (Rice University, 1968.)Google Scholar
(3)Jaco, W.3-Manifolds with fundamental group a free product. Bull. Amer. Math. Soc. 75 (1969), 972–977.CrossRefGoogle Scholar
(4)Kurosh, A. G.The theory of groups II (Chelsea; New York, 1960).Google Scholar
(5)Milnor, J. W.A unique decomposition theorem for 3-manifolds. Amer. J. Math. 84 (1962), 1–7.CrossRefGoogle Scholar
(6)Stallings, J.Grushko's theorem II, Kneser's conjecture. Notices Amer. Math. Soc. 6 (1959), Abstract 559–165, 531–532.Google Scholar
(7)Waldhausen, F.Gruppen mit Zentrum und 3-diruensionale Mannigfaltigkeiten. Topology 6 (1967), 505–517.CrossRefGoogle Scholar