### Using 2-torsion to obstruct topological isotopy

- Series
- Geometry Topology Seminar
- Time
- Monday, March 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 154
- Speaker
- Hannah Schwartz – Bryn Mawr

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.