Generalized ray-singer conjecture. I. A manifold with a smooth boundary (1993).

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Abstract	For my parents Abstract. This paper is devoted to a proof of a generalized Ray-Singer conjecture for a manifold with boundary (the Dirichlet and the Neumann boundary conditions are independently given on each connected component of the boundary and the transmission boundary condition is given on the interior boundary). The Ray-Singer conjecture [RS] claims that for a closed manifold the combinatorial and the analytic torsion norms on the determinant of the cohomology are equal. For a manifold with boundary the ratio between the analytic torsion and the combinatorial torsion is computed. Some new general properties of the Ray-Singer analytic torsion are found. The proof does not use any computation of eigenvalues and its asymptotic expansions or explicit expressions for the analytic torsions of any special classes of manifolds. Contents 1. Analytic torsion and the Ray-Singer conjecture 9 1.1. Analytic and combinatorial torsions norms
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Publisher Date	1993-01-01
Access Restriction	Open
Subject Keyword	Generalized Ray-singer Conjecture Analytic Torsion Manifold Smooth Boundary Neumann Boundary Condition Ray-singer Analytic Torsion Special Class Analytic Torsion Norm Ray-singer Conjecture Explicit Expression Combinatorial Torsion Norm Asymptotic Expansion New General Property Transmission Boundary Condition Closed Manifold Parent Abstract Ray-singer Conjecture R Combinatorial Torsion Interior Boundary
Content Type	Text
Resource Type	Article