From zero surgeries to candidates for exotic definite 4‐manifolds

Author:

Manolescu Ciprian1,Piccirillo Lisa2

Affiliation:

1. Department of Mathematics Stanford University Stanford California USA

2. Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts USA

Abstract

AbstractOne strategy for distinguishing smooth structures on closed 4‐manifolds is to produce a knot in that is slice in one smooth filling of but not slice in some homeomorphic smooth filling . In this paper, we explore how 0‐surgery homeomorphisms can be used to potentially construct exotic pairs of this form. To systematically generate a plethora of candidates for exotic pairs, we give a fully general construction of pairs of knots with the same zero surgeries. By computer experimentation, we find five topologically slice knots such that, if any of them were slice, we would obtain an exotic 4‐sphere. We also investigate the possibility of constructing exotic smooth structures on in a similar fashion.

Funder

National Science Foundation

Publisher

Wiley

Subject

General Mathematics

Reference57 articles.

1. Infinitely many knots admitting the same integer surgery and a four‐dimensional extension;Abe T.;Int. Math. Res. Not.,2015

2. Annulus twist and diffeomorphic 4-manifolds

3. A construction of slice knots via annulus twists

4. On 2-dimensional homology classes of 4-manifolds

5. Cappell-Shaneson homotopy spheres are standard

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Slicing knots in definite 4-manifolds;Transactions of the American Mathematical Society;2024-06-11

2. Trace embeddings from zero surgery homeomorphisms;Journal of Topology;2023-12

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