## Journal of Differential Geometry

### The simple loop conjecture

David Gabai

#### Article information

Source
J. Differential Geom., Volume 21, Number 1 (1985), 143-149.

Dates
First available in Project Euclid: 26 June 2008

https://projecteuclid.org/euclid.jdg/1214439470

Digital Object Identifier
doi:10.4310/jdg/1214439470

Mathematical Reviews number (MathSciNet)
MR806708

Zentralblatt MATH identifier
0556.57007

Subjects
Primary: 57N05: Topology of $E^2$ , 2-manifolds
Secondary: 57M12: Special coverings, e.g. branched

#### Citation

Gabai, David. The simple loop conjecture. J. Differential Geom. 21 (1985), no. 1, 143--149. doi:10.4310/jdg/1214439470. https://projecteuclid.org/euclid.jdg/1214439470

#### References

• [1] I. Berstein and A. Edmonds, On the construction of branched coverings of low-dimensional manifolds, Trans. Amer. Math. Soc. 247 (1979) 87-124.
• [2] I. Berstein and A. Edmonds, On the classification of generic branched coverings of surfaces, Illinois J. Math., 28 (1984) 64-82.
• [3] A. Edmonds, Deformation of maps to branched coverings in dimension two, Ann. of Math. (2) 110 (1979) 113-125.
• [4] D. Gabai, Foliations and the topology of 3-manifolds, J. Differential Geometry 18 (1983) 445-503.
• [5] T. Tucker, On simple loops and surface maps: A correction to Boundary reducible 3-manifolds and Waldhausen's theorem, preprint, 1975, unpublished.