解析挠率在偶数维锥边界上的度规反常
The Metric Anomaly of Analytic Torsion at the Boundary of an Even Dimensional Cone
摘要：
偶数维圆锥的解析挠率公式由三项组成。前两项是很好理解的，并由贝蒂数和锥基的解析挠率的代数组合给出。第三个“奇异”贡献是锥底复杂的谱不变量。第三项是解析挠率的度量反常，它来自于锥在其正则边界上的非积结构。据此，我们滤除了圆锥奇点的实际贡献，并纯粹根据贝蒂数和锥底的解析挠率来确定偶数维圆锥的解析挠率。
英文摘要：
The formula for analytic torsion of a cone in even dimensions is comprised of three terms. The first two terms are well understood and given by an algebraic combination of the Betti numbers and the analytic torsion of the cone base. The third "singular" contribution is an intricate spectral invariant of the cone base. We identify the third term as the metric anomaly of the analytic torsion coming from the non-product structure of the cone at its regular boundary. Hereby we filter out the actual contribution of the conical singularity and identify the analytic torsion of an even-dimensional cone purely in terms of the Betti numbers and the analytic torsion of the cone base.
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