# Using 2-torsion to obstruct topological isotopy

Posted in
Speaker:
Hannah Schwartz
Affiliation:
Bryn Mawr College
Date:
Mon, 2018-10-15 16:30 - 18:00
Location:
MPIM Lecture Hall
Parent event:
MPIM Topology Seminar
It is well known that two knots in S^3 are ambiently isotopic if and only if there is an orientation preserving automorphism of S^3 carrying one knot to the other. In this talk, we will examine a family of smooth 4-manifolds in which the analogue of this fact does not hold, i.e. each manifold contains a pair of smoothly embedded, homotopic 2-spheres that are related by a diffeomorphism, but not smoothly isotopic. In particular, the presence of 2-torsion in the fundamental groups of these 4-manifolds can be used to obstruct even a topological isotopy between the 2-spheres; this shows that Gabai's recent 4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis.
 © MPI f. Mathematik, Bonn Impressum & Datenschutz