Cusp forms and the index theorem for manifolds with boundary

1975 ◽  
Vol 217 (3) ◽  
pp. 221-228
Author(s):  
J. C. Hemperly
Keyword(s):  
Index Theorem ◽  
Cusp Forms ◽  
Manifolds With Boundary

scholarly journals An index theorem for manifolds with boundary

2009 ◽  
Vol 347 (23-24) ◽  
pp. 1393-1398 ◽  
Author(s):  
Paulo Carrillo-Rouse ◽  
Bertrand Monthubert
Keyword(s):  
Index Theorem ◽  
Manifolds With Boundary

Axial anomaly and index theorem for manifolds with boundary

1985 ◽  
Vol 257 ◽  
pp. 199-225 ◽  
Author(s):  
Masao Ninomiya ◽  
Chung-I Tan
Keyword(s):  
Index Theorem ◽  
Manifolds With Boundary ◽  
Axial Anomaly

scholarly journals Index Classes for Vector Fields and their Relation to Certain Characteristic Classes

2013 ◽  
Vol 112 (2) ◽  
pp. 216
Author(s):  
Oskar Hamlet
Keyword(s):  
Vector Fields ◽  
Euler Class ◽  
Index Theorem ◽  
Characteristic Classes ◽  
Manifolds With Boundary

While studying vector fields on manifolds with boundary there are three important indexes to consider. We construct three cohomology classes to compute these. We relate these classes to other classes, the relative Euler class as defined by Sharafutdinov and the secondary Chern-Euler class as defined by Sha. Our results also yield a new proof of the Poincaré-Hopf index theorem.

scholarly journals A cohomological formula for the Atiyah–Patodi–Singer index on manifolds with boundary

2014 ◽  
Vol 06 (01) ◽  
pp. 27-74 ◽  
Author(s):  
P. Carrillo Rouse ◽  
J. M. Lescure ◽  
B. Monthubert
Keyword(s):  
Boundary Condition ◽  
Euclidean Space ◽  
Algebraic Topology ◽  
Normal Bundle ◽  
Pseudodifferential Operators ◽  
Index Theorem ◽  
Manifolds With Boundary ◽  
C Algebras ◽  
Manifold With Boundary ◽  
K Theory

The main result of this paper is a new Atiyah–Singer type cohomological formula for the index of Fredholm pseudodifferential operators on a manifold with boundary. The nonlocality of the chosen boundary condition prevents us to apply directly the methods used by Atiyah and Singer in [4, 5]. However, by using the K-theory of C*-algebras associated to some groupoids, which generalizes the classical K-theory of spaces, we are able to understand the computation of the APS index using classic algebraic topology methods (K-theory and cohomology). As in the classic case of Atiyah–Singer ([4, 5]), we use an embedding into a Euclidean space to express the index as the integral of a true form on a true space, the integral being over a C∞-manifold called the singular normal bundle associated to the embedding. Our formula is based on a K-theoretical Atiyah–Patodi–Singer theorem for manifolds with boundary that is inspired by Connes' tangent groupoid approach, it is not a groupoid interpretation of the famous Atiyah–Patodi–Singer index theorem.

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