楔形奇点流形的Cheeger-Müller定理
A Cheeger-Müller theorem for manifolds with wedge singularities
摘要：
研究退化为楔形奇点流形的闭流形上平坦丛中系数的Hodge Laplacian的谱和热核。提供的霍奇拉普拉斯算子在纤维的楔形有一个适当的谱间隙，我们给出了统一的结构的预解式和热核适当的流形上的角落。当楔形流形和楔形的底都是奇维时，这被用来得到一个Cheeger-Müller定理，该定理将解析挠率与由一个带边界带边流形的自然紧化的Reidemeister挠率联系起来。
英文摘要：
We study the spectrum and heat kernel of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold degenerating to a manifold with wedge singularities. Provided the Hodge Laplacians in the fibers of the wedge have an appropriate spectral gap, we give uniform constructions of the resolvent and heat kernel on suitable manifolds with corners. When the wedge manifold and the base of the wedge are odd dimensional, this is used to obtain a Cheeger-Müller theorem relating analytic torsion with the Reidemeister torsion of the natural compactification by a manifold with boundary.
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