Dehn surgery and A-polynomial for knots

The Property P conjecture states that the 3-manifold Yr obtained by Dehn surgery on a non-trivial knot in S3 with surgery coefficient r ∈ 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 r = ±2 that was the only remaining case to be established for the conjecture. In particular, their results show that the two phenomena of having a cyclic fundamental group and having a homomorphism with non-cyclic image in SU(2) are quite different for 3-manifolds obtained by Dehn fillings. In this paper we extend their results to some other Dehn surgeries via the A-polynomial, and provide more evidence of the ubiquity of the above mentioned phenomena.
Publisher
Taehan Suhakhoe
Issue Date
2006-08
Language
ENG
Citation

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.43, no.3, pp.519 - 529

ISSN
1015-8634
URI
http://hdl.handle.net/10203/87493
Appears in Collection
MA-Journal Papers(저널논문)
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