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A Characterization of T_(2g+1,2) among Alternating Knots

Ni, Yi (2021) A Characterization of T_(2g+1,2) among Alternating Knots. Acta Mathematica Sinica, English Series, 37 (12). pp. 1841-1846. ISSN 1439-8516. doi:10.1007/s10114-021-0408-4.

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Let K be a genus g alternating knot with Alexander polynomial Δ_K(T) = ∑^g_i = _(−g)a_iT^. We show that if |a_g| = |a_(g−1)|, then K is the torus knot T_(2g+1,±2). This is a special case of the Fox Trapezoidal Conjecture. The proof uses Ozsváth and Szabó’s work on alternating knots.

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Alternate Title:A Characterization of T2g+1,2 among Alternating Knots
Additional Information:© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2021. Received July 31, 2020, accepted May 31, 2021. Supported by NSF (Grant No. DMS-1811900).
Funding AgencyGrant Number
Subject Keywords:Alternating knots; Alexander polynomial; strongly quasipositive fibered knots
Issue or Number:12
Classification Code:MR(2010) Subject Classification: 57M25
Record Number:CaltechAUTHORS:20220112-559780400
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Official Citation:Ni, Y. A Characterization of T2g+1,2 among Alternating Knots. Acta. Math. Sin.-English Ser. 37, 1841–1846 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112851
Deposited By: Tony Diaz
Deposited On:12 Jan 2022 23:40
Last Modified:25 Jul 2022 23:14

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