Original Article
Kyungpook Mathematical Journal 2012; 52(3): 245-264
Published online September 23, 2012
Copyright © Kyungpook Mathematical Journal.
Lens Surgeries along the n-twisted Whitehead Link
Teruhisa Kadokami1, Noriko Maruyama2, Masafumi Shimozawa3
1Department of Mathematics, East China Normal University, Dongchuan-lu 500, Shanghai 200241, China
2Musashino Art University, Ogawa 1-736, Kodaira, Tokyo 187-8505, Japan
3Department of Mathematics, Tokyo Woman’s Christian University, Zempukuji 2-6-1, Suginami-ku, Tokyo 167-8585, Japan
Received: September 23, 2012; Revised: September 23, 2012; Accepted: September 23, 2012
We determine lens surgeries (i.e. Dehn surgery yielding a lens space) along the n-twisted Whitehead link. To do so, we first give necessary conditions to yield a lens space from the Alexander polynomial of the link as: (1) n = 1 (i.e. the Whitehead link), and (2) one of surgery coefficients is 1, 2 or 3. Our interests are not only lens surgery itself but also how to apply the Alexander polynomial for this kind of problems.
Keywords: Dehn surgery, lens space, Reidemeister torsion, Alexander polynomial, Rolfsen move