Reidemeister torsion and analytic torsion of discs
Reidemeister torsion and analytic torsion of discs
复制标题
盘的 Reidemeister 扭转和解析扭转
DOI：
10.1007/s10455-011-9300-2
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
M. Spreafico
中科院分区：
文献类型：
--
作者：
L. Hartmann;T. Melo;M. Spreafico
利用Ray和Singer在Cite{RS}中定义的同调的基，研究了欧氏空间中m元维圆盘的Reidomeister挠率和解析挠率.我们证明了Reidemister挠率与圆盘体积的幂重合。利用Cheeger-M{u}ler定理的推广，研究了由边界引起的解析挠率所产生的附加项，利用Bruning和Ma‘cite{bm}证明的公式，在已知项之外预测了一个新的反常边界项，它与边界的欧拉特征成正比.我们的一些结果推广到球面上的锥体的情况，特别是我们直接求出了圆面上的锥体和两个球面上的锥体的解析挠率。我们比较了在低维情况下得到的结果。我们还考虑了Dai和Fang引用{df}给出的一个不同的边界项公式，结果表明用这个公式得到的结果与直接计算解析挠率是不一致的。
We study the Reidemeister torsion and the analytic torsion of the $m$ dimensional disc in the Euclidean $m$ dimensional space, using the base for the homology defined by Ray and Singer in \cite{RS}. We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-M\"{u}ller theorem. We use a formula proved by Br\"uning and Ma \cite{BM}, that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary \cite{Luc}. Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang \cite{DF}, and we show that the result obtained using this formula is inconsistent with the direct calculation of the analytic torsion.