Complex‐valued analytic torsion for flat bundles and for holomorphic bundles with (1,1) connections
Complex‐valued analytic torsion for flat bundles and for holomorphic bundles with (1,1) connections
复制标题
平丛和具有 (1,1) 连接的全纯丛的复值解析扭转
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
E. Y. Miller
中科院分区：
文献类型：
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作者：
S. Cappell;E. Y. Miller
Ray和Singer的工作引入了解析挠率，这是拉普拉斯算子在拓扑和全纯环境中的一种行列式，在这两种环境中自然得到了推广。耦合在拓扑环境中被直接推广到一般的平坦丛，在全纯环境中被推广到具有（1，1）联络的丛，通过使用Newlander-Nirenberg定理，这些丛被看作是具有全纯和反全纯结构的丛。由此得到的拉普拉斯算子的自然推广并不总是自伴的，因此相应的解析挠的推广并不总是真实的值的。关于解析挠率与经典拓扑挠率在拓扑设置中的等价性的Cheeger-Müller定理推广到了这种复值挠率。在代数方面介绍的方法包括一个概念的扭转相关的复杂配备了边界和coboundary地图。© 2009 Wiley Periodicals，Inc.
The work of Ray and Singer that introduced analytic torsion, a kind of determinant of the Laplacian operator in topological and holomorphic settings, is naturally generalized in both settings. The couplings are extended in a direct way in the topological setting to general flat bundles and in the holomorphic setting to bundles with (1,1) connections, which, by using the Newlander‐Nirenberg theorem, are seen to be the bundles with both holomorphic and antiholomorphic structures. The resulting natural generalizations of Laplacians are not always self‐adjoint, and the corresponding generalizations of analytic torsions are thus not always real‐valued. The Cheeger‐Müller theorem on equivalence in a topological setting of analytic torsion to classical topological torsion generalizes to this complex‐valued torsion. On the algebraic side the methods introduced include a notion of torsion associated to a complex equipped with both boundary and coboundary maps. © 2009 Wiley Periodicals, Inc.