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SUMMARY:Non-semisimple link and 3-manifold invariants: on algebraically st
 rong invariants - Azat  Gainutdinov (Centre National de la Recherche Scien
 tifique\, Université de Tours)
DTSTART:20240620T101500Z
DTEND:20240620T111500Z
UID:TALK217399@talks.cam.ac.uk
DESCRIPTION:I will talk about link and 3-manifold invariants defined in te
 rms of a non-semisimple finite ribbon category C together with a choice of
  tensor ideal and a trace on it. If the ideal is all of C\, these invarian
 ts agree with Reshetikhin-Turaev&rsquo\;s link invariants and with 3-manif
 old invariants defined by Lyubashenko in the 90&rsquo\;s\, and as we show\
 , they only depend on the Grothendieck class of the objects labelling the 
 link. These invariants are therefore not able to determine non-split exten
 sions\, or they are algebraically weak. However\, we observed an interesti
 ng phenomenon: if one chooses an intermediate proper ideal between C and t
 he minimal ideal of projective objects\, the invariants become algebraical
 ly much stronger because they do distinguish non-trivial extensions. This 
 is demonstrated in the case of C being the super-modular category of an ex
 terior algebra. That is why these invariants deserve to be called &ldquo\;
 non-semisimple&rdquo\;. This is a joint work with J. Berger and I. Runkel.
LOCATION:External
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