Using 2-torsion to obstruct topological isotopy

Triangle Topology Seminar

Hannah Schwartz (Bryn Mawr College, Mathematics)

Monday, November 5, 2018 -
3:15pm to 4:15pm
Location: 
119 Physics

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.

Last updated: 2018/12/16 - 10:21pm