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Published December 2021 | public
Journal Article

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

Ni, Yi

Abstract

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.

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).

Additional details

Created:
August 22, 2023
Modified:
October 23, 2023