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The Eta Invariant And Families Of Pseudodifferential Operators
 MR 96h:58169
, 1995
"... For a compact manifold without boundary a suspended algebra of pseudodierential operators is considered; it is an algebra of pseudodierential operators on, and translationinvariant in, an additional real variable. ..."
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For a compact manifold without boundary a suspended algebra of pseudodierential operators is considered; it is an algebra of pseudodierential operators on, and translationinvariant in, an additional real variable.
The local index formula in semifinite von Neumann ALGEBRAS II: THE EVEN CASE
, 2004
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The Equivariant Noncommutative AtiyahPatodiSinger Index Theorem ∗
, 2006
"... In [Wu], the noncommutative AtiyahPatodiSinger index theorem was proved. In this paper, we extend this theorem to the equivariant case. Keywords: Equivariant total eta invariants; Clifford asymptotics; C(1)Fredholm module; superconnection. ..."
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In [Wu], the noncommutative AtiyahPatodiSinger index theorem was proved. In this paper, we extend this theorem to the equivariant case. Keywords: Equivariant total eta invariants; Clifford asymptotics; C(1)Fredholm module; superconnection.
Analogues for eta invariants for even dimensional manifolds
, 2011
"... The eta invariant is a secondary geometric invariant, introduced by Atiyah, Patodi and Singer about forty years ago. Ever since, it has been the object of extensive research activity and has found applications in several areas of mathematics and physics. The two results among the rich literature tha ..."
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The eta invariant is a secondary geometric invariant, introduced by Atiyah, Patodi and Singer about forty years ago. Ever since, it has been the object of extensive research activity and has found applications in several areas of mathematics and physics. The two results among the rich literature that are most relevant to this thesis are the AtiyahPatodiSinger twisted index theorem for trivialized flat bundles and the higher AtiyahPatodiSinger index theorem of Getzler and Wu. The former concerns a variational formula for eta invariants on odd dimensional manifolds and its topological interpretation; the latter is a generalization of the AtiyahPatodiSinger L2index theorem for even dimensional manifolds with boundary in the context of cyclic cohomology and its pairing with Ktheory. In this thesis, we shall prove an analogue for each of these two theorems for the case of manifolds of the opposite dimensional parity. Accordingly, the thesis will consist of two parts. In the first part, we prove an analogue for even dimensional manifolds of the
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"... Concentration inequalities and martingale inequalities: a survey. (English summary) Internet Math. 3 (2006), no. 1, 79–127. This survey presents extensions and generalizations of concentration inequalities and martingale inequalities. In this way a rigorous analysis for random graphs with general de ..."
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Concentration inequalities and martingale inequalities: a survey. (English summary) Internet Math. 3 (2006), no. 1, 79–127. This survey presents extensions and generalizations of concentration inequalities and martingale inequalities. In this way a rigorous analysis for random graphs with general degree distributions can be carried out. As an application, concentration of the power law distribution for the infinite Pólya process is analysed. The socalled preferential attachment scheme can be rewritten as a variation of this Pólya process. Reviewed by Dominique Lépingle