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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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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.
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참고문헌 (9)
참고문헌 신청
D. Cooper / 1994 / Plane curvesassociated to character varieties of 3-manifolds 118 (1) : 47 ~ 84
D. Gabai / 1987 / Foliations and the topology of 3-manifolds : 536 ~
L. Moser / 1971 / Elementary surgery along a torus knot 38 : 737 ~
M. Culler / 1987 / Dehn surgery on knots : 300 ~
N. Duneld / 2004 / Non-triviality of theA-polynomial for knots inS3 4 : 1145 ~ 1153
D. Gabai / 1987 / Foliations and the topology of 3-manifolds : 536 ~
L. Moser / 1971 / Elementary surgery along a torus knot 38 : 737 ~
M. Culler / 1987 / Dehn surgery on knots : 300 ~
N. Duneld / 2004 / Non-triviality of theA-polynomial for knots inS3 4 : 1145 ~ 1153
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