Elliptic Boundary Problems for Dirac Operators

1993 ◽  
Author(s):  
Bernhelm Booß-Bavnbek ◽  
Krzysztof P. Wojciechowski
Keyword(s):  
Elliptic Boundary ◽  
Dirac Operators ◽  
Boundary Problems

scholarly journals Higher spectral flow for Dirac operators with local boundary conditions

2016 ◽  
Vol 27 (08) ◽  
pp. 1650068
Author(s):  
Jianqing Yu
Keyword(s):  
Boundary Conditions ◽  
Elliptic Boundary ◽  
Dirac Operators ◽  
Spectral Flow ◽  
Local Boundary ◽  
Manifold With Boundary ◽  
Index Bundle ◽  
Adjoint Extension ◽  
Smooth Map ◽  
Higher Spectral Flow

We consider a one parameter family [Formula: see text] of families of fiberwise twisted Dirac type operators on a fibration with the typical fiber an even dimensional compact manifold with boundary, which verifies [Formula: see text] with [Formula: see text] being a smooth map from the fibration to a unitary group [Formula: see text]. For each [Formula: see text], we impose on [Formula: see text] a certain fixed local elliptic boundary condition [Formula: see text] and get a self-adjoint extension [Formula: see text]. Under the assumption that [Formula: see text] has vanishing [Formula: see text]-index bundle, we establish a formula for the higher spectral flow of [Formula: see text], [Formula: see text]. Our result generalizes a recent result of [A. Gorokhovsky and M. Lesch, On the spectral flow for Dirac operators with local boundary conditions, Int. Math. Res. Not. IMRN (2015) 8036–8051.] to the families case.

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