Complex Valued Analytic Torsion for Flat Bundles and for Holomorphic Bundles with (1,1) Connections

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dc.creatorCappell, Sylvain E.
dc.creatorMiller, Edward Y.
dc.date2008-10-27
dc.date.accessioned2026-07-07T10:13:26Z
dc.date.available2026-07-07T10:13:26Z
dc.descriptionThe work of Ray and Singer which 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 using the Newlander-Nirenberg Theorem are seen to be the bundles with both holomorphic and anti-holomorphic 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-Muller 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 coboundry maps.
dc.description60 pages
dc.identifierhttps://arxiv.org/abs/0810.4833
dc.identifierhttp://arxiv.org/abs/0810.4833
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172528
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject58J52, 53C05, 57R99, 53C55
dc.titleComplex Valued Analytic Torsion for Flat Bundles and for Holomorphic Bundles with (1,1) Connections
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