The Presence of 2-Torsion

The Presence of 2-Torsion

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Hannah Schwartz
Taplin Auditorium

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 (this follows from Cerf's result from the 60's that every orientation preserving automorphism of S^3 is isotopic to the identity). 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 smooothly 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.