论文标题
具有圆锥形奇点的空间的交点扭转和分析扭转
Intersection torsion and analytic torsion of spaces with conical singularities
论文作者
论文摘要
我们证明了Cheeger-Müller定理的扩展到具有孤立的圆锥形奇点的空间：$ l^2 $ - 分析扭转与均匀的尺寸空间上的射线手互动扭转相吻合，它们是微不足道的，而它们的比例在奇怪的空间上是无动的，并且仅在奇异的尺寸上依赖于链接，而链接的链接依赖于该链接。为此，我们在一侧开发了一个组合细胞理论，其同源性与Gregory和MacPherson的相交同源性相吻合，以及在此处定义了Ray-Serger交点扭转。另一方面，我们在具有圆锥形奇点的空间上详细阐述了Hodge-Laplace操作员的光谱理论{\ it Al la} cheeger，并扩展了Hodge理论和分析扭转的经典结果。
We prove an extension of the Cheeger-Müller theorem to spaces with isolated conical singularities: the $L^2$-analytic torsion coincides with the Ray-Singer intersection torsion on an even dimensional space, and they are trivial, while the ratio is non trivial on an odd dimensional space, and the anomaly depends only on the link of the singularities. For this aim, we develop on one side a combinatorial cellular theory whose homology coincides with the intersection homology of Gregory and Macpherson, and where the Ray-Singer intersection torsion is well defined. On the other side, we elaborate the spectral theory for the Hodge-Laplace operator on the square integrable forms on a space with conical singularities {\it á la} Cheeger, and we extend the classical results of the Hodge theory and the analytic torsion.
