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SUMMARY:Extensions of the Abelian Turaev-Viro construction and U(1) BF the
ory to any finite dimensional smooth oriented closed manifold
DTSTART;VALUE=DATE-TIME:20230127T130000Z
DTEND;VALUE=DATE-TIME:20230127T140000Z
DTSTAMP;VALUE=DATE-TIME:20230321T051300Z
UID:indico-event-9305@indico.math.cnrs.fr
DESCRIPTION:Speakers: Philippe Mathieu (Uni Zurich)\n\nIn 1992\, V. Turaev
and O. Viro defined an invariant of smooth oriented closed 3-manifolds co
nsisting of labelling the edges of a triangulation of the manifold with re
presentations of a deformation of the enveloping algebra of sl(2\,C) at a
root of unity\, associating a (quantum) 6j-symbol to each tetrahedron of t
he triangulation\, taking the product of the 6j-symbols over all the tetra
hedra of the manifold\, then summing over all the admissible labelling rep
resentations. It is commonly admitted that this construction is a regulari
zation of a path integral occurring in quantum gravity\, the so-called “
Ponzano-Regge model”\, which is a kind of SU(2) BF gauge theory. A naive
question is: Is it possible to define an abelian version of this invarian
t? If yes\, is there a relation with an abelian BF gauge theory? These que
stions were answered positively in 2016\, and the corresponding Turaev-Vir
o invariant is built from Z/kZ labelling representations (the equivalent o
f 6j-symbols being ``modulo k'' Kronecker symbols) while the associated ga
uge theory is a particular U(1) BF theory (with coupling constant k). This
U(1) BF theory can be straightforwardly extended to any finite dimensiona
l closed oriented manifold\, and so can be the Turaev-Viro construction bu
ilt from Z/kZ labelling representations. A natural question is thus: Are t
hese extensions still related? I will answer this question during the talk
.\n\nhttps://indico.math.cnrs.fr/event/9305/
LOCATION:Fokko du Cloux (Bâtiment Braconnier)
URL:https://indico.math.cnrs.fr/event/9305/
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