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Half-integral finite surgeries on knots in S^3

Li, Eileen and Ni, Yi (2013) Half-integral finite surgeries on knots in S^3. . (Unpublished)

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Suppose that a hyperbolic knot in S^3 admits a finite surgery, Boyer and Zhang proved that the surgery slope must be either integral or half-integral, and they conjectured that the latter case does not happen. Using the correction terms in Heegaard Floer homology, we prove that if a hyperbolic knot in S^3 admits a half-integral finite surgery, then the knot must have the same knot Floer homology as one of eight non-hyperbolic knots which are known to admit such surgeries, and the resulting manifold must be one of ten spherical space forms. As knot Floer homology carries a lot of information about the knot, this gives a strong evidence to Boyer-Zhang's conjecture.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:The second author wishes to thank Xingru Zhang for asking the question about half-integral finite surgery and explaining the background. The second author is also grateful to Liling Gu, whose work [7] benefits our paper a lot. The first author was supported by Caltech’s Summer Undergraduate Research Fellowships program. The second author was partially supported by an AIM Five-Year Fellowship, NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P. Sloan Research Fellowship.
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Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
AIM Five-Year FellowshipUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20150421-115837671
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56819
Deposited By: George Porter
Deposited On:23 Apr 2015 16:34
Last Modified:03 Oct 2019 08:17

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