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Comparing the topological and the smooth 4-genus of satellite knots.


Speaker: Juanita Pinzón Caicedo, University of Notre Dame
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Location: Zoom
Start time: Tue, Nov 3 2020, 1:10PM

The study of 4-dimensional objects is special: a manifold can admit infinitely many non-equivalent smooth structures, and manifolds can be homeomorphic but not diffeomorphic. This difference between topological and smooth structures, can be addressed in terms of the study of knots as boundaries of surfaces embedded in 4D space. In this talk I will focus on some knot operators known as satellites and will show that satellites can bound very different surfaces in the smooth and topological category. This is joint work with Allison Miller and Peter Feller.