## Using 2-torsion to obstruct topological isotopy

Series
Geometry Topology Seminar
Time
Monday, March 11, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Hannah Schwartz – Bryn Mawr
Organizer
John Etnyre
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 are 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.