Seminarium z Topologii Algebraicznej
Wtorki, 12:15-13:45, sala 4070
26.XI.2013
Mark Powell (University of Edinburgh)
Link Slicing and Casson towers
A link is slice if it bounds a collection of disjointly embedded
locally flat discs in the 4-ball. A Casson tower is a 4-manifold with
a fixed attaching circle, built from immersed thickened discs, with
each stage of discs in the tower bounding double point loops of the
discs in the previous stage. Instead of looking for an embedded slice
disc for a link, one can instead try to find a Casson tower bounded by
the link, which might be easier. By work of M. Freedman, a Casson
tower of height 6 contains a locally flat embedded disc. We discuss
various sharpenings of this result involving lower heights which enable
us to give new examples of slice links. Joint with Jae Choon Cha.