Non-semisimple link and 3-manifold invariants: on algebraically strong invariants

Add to your list(s) Download to your calendar using vCal

• Azat Gainutdinov (Centre National de la Recherche Scientifique, Université de Tours)
• Thursday 20 June 2024, 11:15-12:15
• External.

If you have a question about this talk, please contact nobody.

TRHW02 - International Conference

I will talk about link and 3-manifold invariants defined in terms 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 invariants agree with Reshetikhin-Turaev’s link invariants and with 3-manifold invariants defined by Lyubashenko in the 90’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 extensions, or they are algebraically weak. However, we observed an interesting phenomenon: if one chooses an intermediate proper ideal between C and the minimal ideal of projective objects, the invariants become algebraically much stronger because they do distinguish non-trivial extensions. This is demonstrated in the case of C being the super-modular category of an exterior algebra. That is why these invariants deserve to be called “non-semisimple”. This is a joint work with J. Berger and I. Runkel.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• External
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.