论文标题
图八结的彩色琼斯多项式和量子模块化
The colored Jones polynomial of the figure-eight knot and a quantum modularity
论文作者
论文摘要
我们研究$ n $维的有色琼斯的渐近行为，对以$ \ exp \ bigl（（（（U+2p \piı）/n \ bigr）评估的图形结多条件，其中$ u $是一个很小的数量，$ p $是一个积极的integer。我们表明，在$ \ exp \ bigl（4nπ^2/（u+2p \piı）\ bigr）$评估的$ p $二维的琼斯多项式的乘积上等同于渐近的产品，该术语是由Chern-imimimimimient确定的增长率。这表明有色琼斯多项式的量子模块化。
We study the asymptotic behavior of the $N$-dimensional colored Jones polynomial of the figure-eight knot evaluated at $\exp\bigl((u+2p\piı)/N\bigr)$, where $u$ is a small real number and $p$ is a positive integer. We show that it is asymptotically equivalent to the product of the $p$-dimensional colored Jones polynomial evaluated at $\exp\bigl(4Nπ^2/(u+2p\piı)\bigr)$ and a term that grows exponentially with growth rate determined by the Chern--Simons invariant. This indicates a quantum modularity of the colored Jones polynomial.
