DEHN SURGERY AND A-POLYNOMIAL FOR KNOTS

Title & Authors
DEHN SURGERY AND A-POLYNOMIAL FOR KNOTS
Kim, Jin-Hong;

Abstract
The Property P Conjecture States that the 3-manifold $\small{Y_r}$ obtained by Dehn surgery on a non-trivial knot in $\small{S^3}$ with surgery coefficient $\small{{\gamma}{\in}Q}$ has the non-trivial fundamental group (so not simply connected). Recently Kronheimer and Mrowka provided a proof of the Property P conjecture for the case ${\gamma} Keywords Dehn surgery;property P conjecture;A-polynomials; Language English Cited by References 1. D. Cooper, M. Culler, H. Gillet, D. D. Long, and P. B. Shalen, Plane curves associated to character varieties of 3-manifolds, Invent. Math. 118 (1994), no. 1, 47-84 2. M. Culler, C. Gordon, J. Luecke, and P. B. Shalen, Dehn surgery on knots, Ann. of Math. (2) 125 (1987), no. 2, 237-300 3. N. Dunfield and S. Garoufalidis, Non-triviality of the A-polynomial for knots in$S^3\$, Algebr. Geom. Topol. 4 (2004), 1145-1153 (electronic)

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