论文标题
链接和非亚伯雷德氏扭转的自动不变
Holonomy invariants of links and nonabelian Reidemeister torsion
论文作者
论文摘要
我们表明，可以从量子组$ \ mathcal $ \ mathcal {u} _q（\ mathfrak {\ mathfrak {sl} _2 _2 _2）$ for $ q = i $ q = i $ a $ a $ a $ a unity和unity的四个词根中获得，还可以从量子组$ \ mathcal $ \ mathcal $ \ mathcal {u} _q（\ mathcal {u} _q（\ mathcal {u} _q（ $ \ MATHCAL {U} _Q（\ Mathfrak {sl} _2）$满足具有burau代表性的Schur-Weyl二元性。结果，$ \ operatatorName {sl} _2（\ mathbb {c}）$ - 可以作为量子不变的链接扭转链路扭转。我们的构造与Blanchet，Geer，Patureau-Mirand和Reshetikhin的量子自动构成密切相关，我们将它们的不变性解释为扭曲的康威潜力。
We show that the reduced $\mathrm{SL}_2(\mathbb{C})$-twisted Burau representation can be obtained from the quantum group $\mathcal{U}_q(\mathfrak{sl}_2)$ for $q = i$ a fourth root of unity and that representations of $\mathcal{U}_q(\mathfrak{sl}_2)$ satisfy a type of Schur-Weyl duality with the Burau representation. As a consequence, the $\operatorname{SL}_2(\mathbb{C})$-twisted Reidemeister torsion of links can be obtained as a quantum invariant. Our construction is closely related to the quantum holonomy invariant of Blanchet, Geer, Patureau-Mirand, and Reshetikhin, and we interpret their invariant as a twisted Conway potential.
