논문KCI 등재
Dehn surgery and SA$-ploynomial for knots
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Abstract
The PropertyP conjecture states that the 3-manifoldYr obtained by Dehn surgery on a non-trivial knot in S3 withsurgery coecient r 2 Q has the non-trivial fundamental group(so not simply connected). Recently Kronheimer and Mrowka pro-vided a proof the Property P conjecture for the caser = 2 thatwas the only remaining case to be established for the conjecture.In particular, their results show that the two phenomena of havinga cyclic fundamental group and having a homomorphism with non-cyclic image in SU(2) are quite dierent for 3-manifolds obtainedby Dehn llings. In this paper we extend their results to some otherDehn surgeries via theA-polynomial, and provide more evidence ofthe ubiquity of the above mentioned phenomena.
참고문헌 (9)
- D. Cooper, "Plane curvesassociated to character varieties of 3-manifolds", 118(1), pp.47~84 (1994)
- M. Culler, "Dehn surgery on knots", pp.300~ (1987)
- N. Duneld, "Non-triviality of theA-polynomial for knots inS3", 4, pp.1145~1153 (2004)
- D. Gabai, "Foliations and the topology of 3-manifolds", pp.536~ (1987)
- P. B. Kronheimer, "Witten's conjecture and Property", 8, pp.295~310 (2004)
- _, "Dehn surgery, the fundamental group and SU(2) preprint" (2004)
- T. S. Mrowka, "To appear in Ann. Math", mo(ploes and lens space surgeries)
- L. Moser, "Elementary surgery along a torus knot", 38, pp.737~ (1971)
- P. Ozsv\' ath, "Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary", 173(2), pp.179~261 (2003)
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