理想Turaev-Viro不变量
Ideal Turaev-Viro invariants
摘要：
Turaev-Viro不变量是状态和，即，一个多项式，可以从一个特殊的脊柱或一个紧凑的3-流形的三角剖分读出。如果多项式在某个多项式方程（Biedenharn-Elliott方程）的解处求值，则结果是流形的同胚不变量（"数值Turaev-Viro不变量“）。方程系统定义了一个理想，实际上多项式关于该理想的陪集也是同胚不变量（“理想Turaev-Viro不变量”）。很明显，理想的Turaev-Viro不变量至少与数值Turaev-Viro不变量一样强，我们有理由期望它们严格更强。他们提供了一个更统一的方法，因为许多数值Turaev-Viro不变量可以捕获在一个单一的理想Turaev-Viro不变量。利用计算机代数，我们得到了计算结果的一些例子的理想Turaev-Viro不变量。
英文摘要：
A Turaev-Viro invariant is a state sum, i.e., a polynomial that can be read off from a special spine or a triangulation of a compact 3-manifold. If the polynomial is evaluated at the solution of a certain system of polynomial equations (Biedenharn-Elliott equations) then the result is a homeomorphism invariant of the manifold (``numerical Turaev-Viro invariant''). The equation system defines an ideal, and actually the coset of the polynomial with respect to that ideal is a homeomorphism invariant as well (``ideal Turaev-Viro invariant''). It is clear that ideal Turaev-Viro invariants are at least as strong as numerical Turaev-Viro invariants, and we show that there is reason to expect that they are strictly stronger. They offer a more unified approach, since many numerical Turaev-Viro invariants can be captured in a singly ideal Turaev-Viro invariant. Using computer algebra, we obtain computational results on some examples of ideal Turaev-Viro invariants.
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。
