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Speaker:

L. Lewark
Affiliation:

Inst. de Math. de Jussieu\MPI
Date:

Thu, 22/05/2014 - 15:00 - 16:00
Location:

MPIM Lecture Hall
Parent event:

MPI-Oberseminar 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 Poincaré 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.

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