An extended Cheeger–Müller theorem for covering spaces
An extended Cheeger–Müller theorem for covering spaces
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DOI：
10.1016/j.top.2005.04.001
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发表时间：
2005-11
期刊：
影响因子：
--
通讯作者：
Weiping Zhang
中科院分区：
文献类型：
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作者：
Weiping Zhang
本文将Bismut-Zhang的一个定理推广到无限Galois覆盖空间，该定理将Cheeger-Müller关于Ray-Singer挠和Reidemeister挠的定理推广到无限Galois覆盖空间.我们的结果是在扩展上同调的框架下得到的，推广了Braverman-Carey-Farber-Mathai的一个结果.它不使用行列式类条件，因此也（潜在地）推广了Burghelea，Friedlander，Kappeler和McDonald关于L2-挠的几个结果。我们将Braverman-Carey-Farber-Mathai关于扩张上同调行列式的框架与Bismut-Zhang的原始论文中提出的热核方法结合起来，联合收割机证明了我们的结果.
We generalize a theorem of Bismut–Zhang, which extends the Cheeger–Müller theorem on Ray–Singer torsion and Reidemeister torsion, to the case of infinite Galois covering spaces. Our result is stated in the framework of extended cohomology, and generalizes in this case a recent result of Braverman–Carey–Farber–Mathai. It does not use the determinant class condition and thus also (potentially) generalizes several results on L2-torsions due to Burghelea, Friedlander, Kappeler and McDonald. We combine the framework developed by Braverman–Carey–Farber–Mathai on the determinant of extended cohomology with the heat kernel method developed in the original paper of Bismut–Zhang to prove our result.