منابع مشابه
Entropy, Determinants, and L-torsion
We show that for any amenable group Γ and any ZΓ-module M of type FL with vanishing Euler characteristic, the entropy of the natural Γ-action on the Pontryagin dual of M is equal to the L-torsion of M. As a particular case, the entropy of the principal algebraic action associated with the module ZΓ/ZΓf is equal to the logarithm of the Fuglede-Kadison determinant of f whenever f is a non-zero-di...
متن کاملEntropy , Determinants , and L 2 - Torsion
We show that for any amenable group Γ and any ZΓ-module M of type FL with vanishing Euler characteristic, the entropy of the natural Γ-action on the Pontryagin dual of M is equal to the L-torsion of M. As a particular case, the entropy of the principal algebraic action associated with the module ZΓ/ZΓf is equal to the logarithm of the Fuglede-Kadison determinant of f whenever f is a non-zero-di...
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We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of ...
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We tackle the inverse problem of reconstructing an unknown finite measure μ from a noisy observation of a generalized moment of μ defined as the integral of a continuous and bounded operator Φ with respect to μ . When only a quadratic approximation Φm of the operator is known, we introduce the L2 approximate maximum entropy solution as a minimizer of a convex functional subject to a sequence of...
متن کاملTuraev Torsion and Cohomology Determinants for 3-Manifolds with Boundary
We obtain generalizations of some results of Turaev from [Tur02]. Turaev’s results relate leading order terms of the Turaev torsion of closed, oriented, connected 3–manifolds to certain “determinants” derived from cohomology operations such as the alternate trilinear form on the first cohomology group given by cup product. These determinants unfortunately do not generalize directly to compact, ...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2013
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2013-00778-x