Geometry and Topology Seminar

  Surfaces in a 4-manifold can be topologically isotopic, but not smoothly isotopic. In this talk, we will discuss a new method for constructing such "exotic" embeddings of tori. The novel feature of this construction is that our tori are topologically trivial (topologically bound a solid torus in the 4-manifold), but smoothly non-trivial. We will also show that this construction (and in fact allknown constructions of exotically embedded surfaces) are fragile. Specifically, they become smoothly isotopic again after increasing the genus by adding a single handle. Parts of this work are joint with  Neil Hoffman and Inanc Baykur.