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Exotic Nonleaves with Infinitely Many Ends.

Authors :
Cotón, Carlos Meniño
Schweitzer, Paul A
Source :
IMRN: International Mathematics Research Notices. Jul2022, Vol. 2022 Issue 14, p10912-10951. 40p.
Publication Year :
2022

Abstract

We show that any simply connected topological closed |$4$| -manifold punctured along any compact, totally disconnected tame subset |$\Lambda $| admits a continuum of smoothings, which are not diffeomorphic to any leaf of a |$C^{1,0}$| codimension one foliation on a compact manifold. This includes the remarkable case of |$S^4$| punctured along a tame Cantor set. This is the lowest reasonable regularity for this realization problem. These results come from a new criterion for nonleaves in |$C^{1,0}$| regularity. We also include a new criterion for nonleaves in the |$C^2$| -category. Some of our smooth nonleaves are "exotic", that is, homeomorphic but not diffeomorphic to leaves of codimension one foliations on a compact manifold, being the 1st examples in this class. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10737928
Volume :
2022
Issue :
14
Database :
Academic Search Index
Journal :
IMRN: International Mathematics Research Notices
Publication Type :
Academic Journal
Accession number :
158324048
Full Text :
https://doi.org/10.1093/imrn/rnab042