利用子因子计算三维流形的Turaev-Viro-Ocneanu不变量
Computations of Turaev-Viro-Ocneanu invariants of 3-manifolds from subfactors
摘要：
本文建立了两个管代数之间的严格对应关系，一个来自于Ocneanu引入的Turaev-Viro-Ocneanu TQFT，另一个来自于Izumi引入的扇形理论，并在两个管代数的中心之间构造了一个标准同构，这是一个保两个代数的乘积并与SL（2，Z）的作用交换的共轭线性同构.通过这种对应关系和Dehn手术公式，我们利用Izumi的扇区数据，计算了基本三维流形（包括透镜空间和Brieskorn三维流形）的Turaev-Viro-Ocneanu不变量.
英文摘要：
In this paper, we establish a rigorous correspondence between the two tube algebras, that one comes from the Turaev-Viro-Ocneanu TQFT introduced by Ocneanu and another comes from the sector theory introduced by Izumi, and construct a canonical isomorphism between the centers of the two tube algebras, which is a conjugate linear isomorphism preserving the products of the two algebras and commuting with the actions of SL(2,Z). Via this correspondence and the Dehn surgery formula, we compute Turaev-Viro-Ocneanu invariants from several subfactors for basic 3-manifolds including lens spaces and Brieskorn 3-manifolds by using Izumi's data written in terms of sectors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
