Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

L. Lewark
Affiliation:

Inst. de Math. de Jussieu\MPI
Date:

Thu, 2014-05-22 15:00 - 16:00 A knot is called smoothly slice if it bounds a disc smoothly embedded into the four-ball. Requiring the disc's embedding to be locally flat instead of smooth leads to the definition of a topologically slice knot. There are topologically slice knots that are not smoothly slice. Such knots could be used to construct a counterexample refuting the smooth four-dimensional PoincarĂ© conjecture. We will see a large family of obstructions to smooth sliceness, which are able to show the existence of such knots, arising from a theory which is combinatorial and has its roots in representation theory: the Khovanov-Rozansky knot homologies, categorifications of Reshetikhin and Turaev's sl(n)-polynomials. The talk will begin with an introduction to the slice genus and Khovanov-Rozansky homologies, and finish with the spectral sequences that are our main tool in the analysis of those homologies.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/158