Back to Search
Start Over
From zero surgeries to candidates for exotic definite 4‐manifolds.
- Source :
-
Journal of the London Mathematical Society . Nov2023, Vol. 108 Issue 5, p2001-2036. 36p. - Publication Year :
- 2023
-
Abstract
- One strategy for distinguishing smooth structures on closed 4‐manifolds is to produce a knot K$K$ in S3$S^3$ that is slice in one smooth filling W$W$ of S3$S^3$ but not slice in some homeomorphic smooth filling W′$W^{\prime }$. 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 #nCP2$\#^n \mathbb {CP}^2$ in a similar fashion. [ABSTRACT FROM AUTHOR]
- Subjects :
- *KNOT theory
*HOMEOMORPHISMS
*SURGERY
*POSSIBILITY
*COMPUTERS
Subjects
Details
- Language :
- English
- ISSN :
- 00246107
- Volume :
- 108
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 173552159
- Full Text :
- https://doi.org/10.1112/jlms.12800