论文标题
扭曲的Ruelle Zeta功能在双曲线歧管和复杂值分析扭转上
Twisted Ruelle zeta function on hyperbolic manifolds and complex-valued analytic torsion
论文作者
论文摘要
在本文中，我们研究了与紧凑的，双曲线，奇异的歧管$ x $相关的扭曲的ruelle zeta功能。扭曲的ruelle zeta函数与无环表示$χ\colonπ_{1}（x）\ rightArrow \ gl_ {n}（\ c）$相关联，该\ gl_ {n}（\ c）$足够接近acyclic，单位表示。在这种情况下，扭曲的ruelle Zeta功能是零的，等于精制的分析扭转的平方，因为Braverman和Kappeler在\ cite {BK2}中介绍了它，乘以指数，该指数涉及ETA的eTa不变型，涉及与奇数 - 符号的一部分，与奇数 - 符号的一部分相关。
In this paper, we study the twisted Ruelle zeta function associated with the geodesic flow of a compact, hyperbolic, odd-dimensional manifold $X$. The twisted Ruelle zeta function is associated with an acyclic representation $χ\colon π_{1}(X) \rightarrow \GL_{n}(\C)$, which is close enough to an acyclic, unitary representation. In this case, the twisted Ruelle zeta function is regular at zero and equals the square of the refined analytic torsion, as it is introduced by Braverman and Kappeler in \cite{BK2}, multiplied by an exponential, which involves the eta invariant of the even part of the odd-signature operator, associated with $χ$.
