![]() ![]() (There’s even an “if and only if” statement). In a parallel to Freedman’s famous result that all knots with trivial Alexander polynomial are algebraically slice, it turns out that the vanishing of certain knot invariants implies that such a spherical generator exists, at least in the topological category. This manifold is homotopy equivalent to a 2-sphere, and so it is natural to ask when it has an embedded spherical generator for second homology. Title: Embedding spheres in simple 4-manifoldsĪbstract:Given a knot K and an integer n, there is an associated nice 4-manifold called the n-trace of K. Finally we’ll explain how gauge theory and symplectic topology show that most smoothable simply-connected 4-manifolds are ample, and why this implies that they have stable homologically ample smoothings (this is joint work with Auckly, Kim and Ruberman). We will then introduce what it means for a topological 4-manifold to be ample – meaning roughly that it has loads of smooth structures – and for a smooth 4-manifold to be homologically ample – meaning its primitive ordinary homology classes can be represented by lots of smoothly embedded spheres. Symplectic 4-manifolds on the Noether line and between the Noether and half Noether linesĪbstract: This talk will begin with a review of some standard notions of stabilization of 4-manifolds, two celebrated results of Wall from the 1960s, and Freedman’s topological classification of closed, oriented simply-connected 4-manifolds from the 1980s. So please update your zoom application to the latest version so you will be able to freely move between the breakout rooms! Monday 10:00-10:10 On Tuesday and Wednesday they will focus on the lightning talks, and on other days on either the mini-courses or research talks. ![]() Titles and abstracts for the research talk and the lightning talks can be found below.ĭuring the lunch sessions, from 12:30 to 1:00 we will have several breakout rooms set up where people can go to chat and discuss the talks and mini-courses. You can find videos of the research talks here.ĭetails about the mini-courses can be found here. During two of the lunch sessions we will have breakout rooms so you can discuss with the lightning speakers. We have split the office hours for each course into a morning and after noon session to hopefully accommodate people form a variety of time zones. The remainder of the mini-courses will be held synchronously during the summer school. Here are the lectures for Piccirillo, Ray, and Stipsicz. (Probably best to watch the first Stipsicz lecture before the others.) On the first day of the workshop there will be time to ask the speakers questions about these talks and the homework they suggested in the talks. Please watch the first two lectures from each mini-course. ![]()
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