论文标题
从亚历山大多项式方面
Generalized Bott-Cattaneo-Rossi invariants in terms of Alexander polynomials
论文作者
论文摘要
The Bott-Cattaneo-Rossi invariant $(Z_k)_{k\in \mathbb N\setminus\{0,1\}}$ is an invariant of long knots $\mathbb R^n\hookrightarrow\mathbb R^{n+2}$ for odd $n$, which reads as a combination of integrals over configuration spaces.在本文中，我们计算了此类积分并证明（广义）$ z_k $在Alexander多项式方面，或者是在链接一个由结端的某些循环的数字方面的。我们的公式适用于所有无效的同源性$ \ mathbb r^{n+2} $至少在$ n \ equiv 1 \ mod 4 $时，相反，以$（z_k）_ {k {k in \ mathbb n \ setminus n \ in \ in \ setminus} 0. 0.11的reidemeister torseys表示。我们的公式扩展到了均匀的案例，在即将发表的文章中，$ z_k $将被证明是明确的。
The Bott-Cattaneo-Rossi invariant $(Z_k)_{k\in \mathbb N\setminus\{0,1\}}$ is an invariant of long knots $\mathbb R^n\hookrightarrow\mathbb R^{n+2}$ for odd $n$, which reads as a combination of integrals over configuration spaces. In this article, we compute such integrals and prove explicit formulas for (generalized) $Z_k$ in terms of Alexander polynomials, or in terms of linking numbers of some cycles of a hypersurface bounded by the knot. Our formulas, which hold for all null-homologous long knots in homology $\mathbb R^{n+2}$ at least when $n\equiv 1\mod 4$, conversely express the Reidemeister torsion of the knot complement in terms of $(Z_k)_{k\in\mathbb N\setminus\{0,1\}}$. Our formula extends to the even-dimensional case, where $Z_k$ will be proved to be well-defined in an upcoming article.
