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Online Seminar: A universal state sum May 21, 2020 (10:00 AM PDT - 11:00 AM PDT)
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Location: MSRI: Online/Virtual
Speaker(s) Kevin Walker (Microsoft Research Station Q)
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A Universal State Sum


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Given a sufficiently nice n-pivotal n-category, I'll describe an explicit state sum invariant for oriented n+1-dimensional manifolds.  ("Sufficiently nice" refers to some finiteness and semisimplicity conditions; "n-pivotal" means pivotal for n=2 and something analogous for higher n.)  The construction also works for unoriented, Spin and Pin manifolds.  The universal state sum specializes to a long list of familiar state sums: Turaev-Viro, Crane-Yetter, Douglas-Reutter, Reshitikhin-Turaev Dehn surgery formula (thought of as a state sum), Brown-Arf (for Pin_- 2-manifolds), Dijkgraaf-Witten.

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A Universal State Sum

H.264 Video 24994_28346_8359_A_Universal_State_Sum.mp4