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Annulus twist and diffeomorphic 4-manifolds

Published online by Cambridge University Press:  17 May 2013

TETSUYA ABE ,
IN DAE JONG ,
YUKA OMAE  and
MASANORI TAKEUCHI
TETSUYA ABE
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan. e-mail: tetsuya@kurims.kyoto-u.ac.jp
IN DAE JONG
Affiliation:
Faculty of Liberal Arts and Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan. e-mail: jong@las.osakafu-u.ac.jp
YUKA OMAE
Affiliation:
Osaka Prefectural Kitano High School, Osaka 532-0025, Japan. e-mail: T-OmaeYu@medu.pref.osaka.jp
MASANORI TAKEUCHI
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan.
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Abstract

We give a method for obtaining infinitely many framed knots which represent a diffeomorphic 4-manifold. We also study a relationship between the n-shake genus and the 4-ball genus of a knot. Furthermore we give a construction of homotopy 4-spheres from a slice knot with unknotting number one.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 2 , September 2013 , pp. 219 - 235
Copyright
Copyright © Cambridge Philosophical Society 2013 

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