Dehn surgery and SA$-ploynomial for knots

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 t...

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Published in:Taehan Suhakhoe hoebo 2006, 43(3), , pp.519-529
Main Author: 김진홍
Format: Article
Language:Korean
Subjects:
수학
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Summary: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. KCI Citation Count: 0
ISSN:1015-8634
2234-3016