Property P for knots admitting certain Gabai disks

We show that if a knot has a minimal spanning surface that admits certain Gabai disks, then a manifold obtained by ±1-Dehn surgery along the knot has infinite fundamental group. As one of the applications we extend and simplify a recent result of Menasco and Zhang that closed 3-braid knots have Prop...

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Bibliographic Details
Published in:Topology and its applications 2004-07, Vol.142 (1), p.113-129
Main Authors: Dasbach, Oliver T., Li, Tao
Format: Article
Language:English
Subjects:
Boundary slope
Branched surface
Casson invariant
Lamination
Property P
Train track
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Summary:We show that if a knot has a minimal spanning surface that admits certain Gabai disks, then a manifold obtained by ±1-Dehn surgery along the knot has infinite fundamental group. As one of the applications we extend and simplify a recent result of Menasco and Zhang that closed 3-braid knots have Property P. Other applications are given.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2003.11.010