0cobordance of 2spheres in the 4sphere
0cobordance of 2spheres in the 4sphere

Jason Joseph, Rice University
Fine Hall 314
Embedded 2spheres K and J in the 4sphere are 0cobordant if they are joined in S^4 x I by an orientable 3manifold M, such that each regular level set of M is a collection of 2spheres. Ogasa introduced a local 0cobordism called a ribbon move, and found several obstructions to ribbon move equivalence. In this talk we go from local to global by proving that K and J are 0cobordant if and only if they are ribbon move equivalent. This means that Ogasa’s invariants obstruct 0cobordance as well: in particular, there are infinitely many 0cobordism classes of 2knots. We also apply this theorem to the isotopy of unit spheres in CP^2.
This is joint work with Hannah Schwartz.