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New quantum obstructions to sliceness

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Speaker: 
L. Lewark
Affiliation: 
Inst. de Math. de Jussieu\MPI
Date: 
Thu, 2014-05-22 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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