 

Terry A. Loring and Hermann SchulzBaldes
Finite volume calculation of Ktheory invariants view print


Published: 
August 29, 2017

Keywords: 
Ktheory, spectral flow, topological insulator 
Subject: 
46L80, 19K56, 58J28 


Abstract
Odd index pairings of K_{1}group elements with Fredholm modules are of relevance in index theory, differential geometry and applications such as to topological insulators. For the concrete setting of operators on a Hilbert space over a lattice, it is shown how to calculate the resulting index as the signature of a suitably constructed finitedimensional matrix, more precisely the finite volume restriction of what we call the spectral localizer. In presence of real symmetries, secondary Z_{2}invariants can be obtained as the sign of the Pfaffian of the spectral localizer. These results reconcile two complementary approaches to invariants of topological insulators.


Acknowledgements
The first author was in part supported by a grant from the Simons Foundation (#419432). The second author was in part supported by the DFG


Author information
Terry A. Loring:
Department of Mathematics and Statistics, University of New Mexico, USA
loring@math.unm.edu
Hermann SchulzBaldes:
Department Mathematik, FriedrichAlexanderUniversität ErlangenNürnberg, Germany
schuba@mi.unierlangen.de

