Index Theory for Generalized Dirac Operators on Open Manifolds

2006 ◽  
pp. 73-128 ◽  
Author(s):  
Jürgen Eichhorn
Keyword(s):  
Index Theory ◽  
Dirac Operators ◽  
Open Manifolds

scholarly journals Index Theory and Non-Commutative Geometry II. Dirac Operators and Index Bundles

2007 ◽  
Vol 1 (2) ◽  
pp. 305-356 ◽  
Author(s):  
Moulay-Tahar Benameur ◽  
James L. Heitsch
Keyword(s):  
Chern Character ◽  
Index Theory ◽  
Dirac Operators ◽  
Type Operator ◽  
Index Formula ◽  
Dirac Type ◽  
Dirac Type Operator ◽  
Index Bundle

AbstractWhen the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chern character in Haefliger cohomology and relate it to the Chern character of the K—theory index. This result gives a concrete connection between the topology of the foliation and the longitudinal index formula. Moreover, the usual spectral assumption on the Novikov-Shubin invariants of the operator is improved.

scholarly journals Two-cocycle twists and Atiyah–Patodi–Singer index theory

2018 ◽  
Vol 167 (3) ◽  
pp. 437-487 ◽  
Author(s):  
SARA AZZALI ◽  
CHARLOTTE WAHL
Keyword(s):  
Fundamental Group ◽  
Scalar Curvature ◽  
Index Theory ◽  
Dirac Operators ◽  
Index Theorem ◽  
Universal Covering ◽  
Positive Scalar Curvature ◽  
Spin Manifolds ◽  
Projective Action

AbstractWe construct η- and ρ-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah–Patodi–Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.

Higher Index Theory

2020 ◽  
Author(s):  
Rufus Willett ◽  
Guoliang Yu
Keyword(s):  
Index Theory
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