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SUMMARY:David Reutter (MPI Bonn)
DTSTART:20210219T170000Z
DTEND:20210219T180000Z
DTSTAMP:20260423T040006Z
UID:TQFT/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TQFT/30/">Se
 misimple topological field theories in even dimensions</a>\nby David Reutt
 er (MPI Bonn) as part of Topological Quantum Field Theory Club (IST\, Lisb
 on)\n\n\nAbstract\nA major open problem in quantum topology is the constru
 ction of an oriented 4-dimensional topological quantum field theory (TQFT)
  in the sense of Atiyah-Segal which is sensitive to exotic smooth structur
 e. More generally\, how much manifold topology can a TQFT see? \n\nIn this
  talk\, I will answer this question for semisimple field theories in even 
 dimensions — I will sketch a proof that such field theories can at most 
 see the stable diffeomorphism type of a manifold and conversely\, that if 
 two sufficiently finite manifolds are not stably diffeomorphic then they c
 an be distinguished by semisimple field theories. In this context\, `semis
 implicity' is a certain algebraic condition applying to all currently know
 n examples of vector-space-valued TQFTs\, including `unitary field theorie
 s’\, and `once-extended field theories' which assign algebras or linear 
 categories to codimension 2 manifolds. I will discuss implications in dime
 nsion 4\, such as the fact that oriented semisimple field theories cannot 
 see smooth structure\, while unoriented ones can. \n\nThroughout\, I will 
 use the Crane-Yetter field theory associated to a ribbon fusion category\,
  as a guiding example.\n\nThis is based on arXiv:2001.02288 and joint work
  in progress with Chris Schommer-Pries.\n
LOCATION:https://researchseminars.org/talk/TQFT/30/
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