Analytic torsion and R-torsion of Riemannian manifolds
Analytic torsion and R-torsion of Riemannian manifolds
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DOI：
10.1016/0001-8708(78)90116-0
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发表时间：
1978-06
影响因子：
1.7
通讯作者：
W. Müller
中科院分区：
文献类型：
--
作者：
W. Müller
本文的主要目的是证明关于挠1的Ray-Singer猜想。设X是一个N维无边界的紧定向Cm黎曼流形，K是X的光滑三角剖分的单纯复形。在微分拓扑学的许多问题中，当一个非平凡的基本群出现时，会很自然地产生一个拓扑不变量，即所谓的Reidemeister-Franz挠率（R-挠率）T~，它是关于三角剖分K和基本群rl（X）的一个给定的正交矩阵O（n）表示p定义的。关于它的定义，请参阅第6节。考虑到Atiyah-Singer指数定理，很自然地会问R-挠率7 x是否有一个与拓扑挠率相等的解析对应物。这个问题是由Ray和Singer [19]提出的，他们引入了De Rham复形的不变量
The main purpose of this paper is to prove the Ray-Singer conjecture concerning torsion1Let X be a compact oriented Cm Riemannian manifold of dimension N without boundary and let K be the simplicial complex of a smooth triangulation of X. In many problems of differential topology, where a nontrivial fundamental group occurs, there arises very naturally a certain topological invariant, the so-called Reidemeister-Franz torsion (R-torsion) T~, which is defined with respect to the triangulation K and a given representation p of the fundamental group rl (X) by orthogonal matrices O (n). For its definition we refer to Section 6. With the Atiyah-Singer index theorem in mind, it is very natural to ask whether the R-torsion 7x has an analytic counterpart which is equal to the topological one. This question was raised by Ray and Singer [19], who introduced an invariant of the De Rham complex