A construction of slice knots via annulus modifications

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We define an operation on a homology B-4 that we call an n-twist annulus modification. We give a new construction of smoothly slice knots and exotically slice knots via n-twist annulus modifications. As an application, we present a new example of a smoothly slice knot with non-slice derivatives. Such examples were first discovered by Cochran and Davis. Also, we relate n-twist annulus modifications to n-fold annulus twists which was first introduced by Osoinach and has been used by Abe and Tange to construct smoothly slice knots. Furthermore we show that any exotic slice disk can be obtained by an annulus modification performed on some exotic slice disk bounding the unknot. (C) 2018 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2018-04
Language
English
Article Type
Article
Citation

TOPOLOGY AND ITS APPLICATIONS, v.238, pp.1 - 19

ISSN
0166-8641
DOI
10.1016/j.topol.2018.01.010
URI
http://hdl.handle.net/10203/280219
Appears in Collection
MA-Journal Papers(저널논문)
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