منابع مشابه
Eta Invariant and Conformal Cobordism
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 ...
متن کاملAbsolute Torsion and Eta-invariant
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...
متن کاملJumps of the Eta-invariant
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...
متن کاملBoundaries, Eta Invariant and the Determinant Bundle
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 ...
متن کاملThe Eta Invariant and Families of Pseudodifferential Operators
For a compact manifold without boundary a suspended algebra of pseudodifferential operators is considered; it is an algebra of pseudodifferential operators on, and translation-invariant in, an additional real variable. It is shown that the eta invariant, as defined by Atiyah, Patodi and Singer for admissible Dirac operators, extends to a homomorphism from the ring of invertible elements of the ...
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ژورنال
عنوان ژورنال: Annals of Global Analysis and Geometry
سال: 2005
ISSN: 0232-704X,1572-9060
DOI: 10.1007/s10455-005-6494-1