Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group
Geometric Topology
2024-07-24 v2
Abstract
We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2-spheres in simply connected 4-manifolds, which are topologically isotopic and whose complement has a prescribed fundamental group that satisfies some conditions. This class of groups include finite cyclic groups and the binary icosahedral group. These are the first known examples of knotting phenomena in 4-manifolds with such properties. Examples of locally flat embedded 2-spheres in non-smoothable 4-manifolds are also given.
Keywords
Cite
@article{arxiv.2204.10089,
title = {Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group},
author = {Rafael Torres},
journal= {arXiv preprint arXiv:2204.10089},
year = {2024}
}
Comments
v2: incorporated referee's suggestions. Final version