Institute of Mathematics for Industry


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On the state sum invariants of 3-manifolds constructed from a $E_6$ linear skein

Hold Date 2013-10-04 16:00~2013-10-04 17:00

Place Seminar Room 1, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Kenta OKAZAKI (Kyoto University, RIMS)

The state sum invariants are invariants of 3-manifolds. Turaev and Viro defined the state sum invariants by using "$6j$-symbols" arising from the representations of the quantum group. Ocneanu generalized their invariants to ones which are constructed from $6j$-symbols of subfactors.

In this talk, we introduce a linear skein of planar graphs, in some sense, in order to reconstruct the state sum invariants associated with the $E_6$ subfactor, and give an elementary proof of the invariance. We also compute the state sum invariants of all the lens spaces from our reconstruction.