منابع مشابه
Geodesic Conjugacy in Two - Step Nilmanifolds
Two Riemannian manifolds are said to have C-conjugate geodesic flows if there exist an C diffeomorphism between their unit tangent bundles which intertwines the geodesic flows. We obtain a number of rigidity results for the geodesic flows on compact 2-step Riemannian nilmanifolds: For generic 2-step nilmanifolds the geodesic flow is C rigid. For special classes of 2-step nilmanifolds, we show t...
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In 2], Atiyah, Patodi and Singer introduced an invariant D of any self-adjoint elliptic diierential operator D on an odd-dimensional oriented closed manifold M, in order to prove an index theorem for manifolds with boundary. For the germi-nal case of the \signature operator"the relevant D is (d ? d), where the Hodge duality operator is determined by the Reimannian metric on M. They consider, mo...
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In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an Abelian group, the conformal cobordism group, which classifies the conformally flat structures according to whether they bound conformally flat structures in a conformally invariant way. The eta invariant ...
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In a recent joint work with V. Turaev [6], we defined a new concept of combinatorial torsion which we called absolute torsion. Compared with the classical Reidemeister torsion, it has the advantage of having a well-determined sign. Also, the absolute torsion is defined for arbitrary orientable flat vector bundles, and not only for unimodular ones, as is classical Reidemeister torsion. In this p...
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Cobordism invariance shows that the index, in K-theory, of a family of pseudodifferential operators on the boundary of a fibration vanishes if the symbol family extends to be elliptic across the whole fibration. For Dirac operators with spectral boundary condition, Dai and Freed [5] gave an explicit version of this at the level of the determinant bundle. Their result, that the eta invariant of ...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2018
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2018.v26.n2.a2