Geodesic
Spectral Flow Argument Localizing an Odd Index Pairing
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 373-381

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DOI

An odd Fredholm module for a given invertible operator on a Hilbert space is specified by an unbounded so-called Dirac operator with compact resolvent and bounded commutator with the given invertible. Associated with this is an index pairing in terms of a Fredholm operator with Noether index. Here it is shown by a spectral flow argument how this index can be calculated as the signature of a finite dimensional matrix called the spectral localizer.
DOI : 10.4153/CMB-2018-013-x
Mots-clés : index pairing, spectral flow, topological materials 
Loring, Terry A.; Schulz-Baldes, Hermann. Spectral Flow Argument Localizing an Odd Index Pairing. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 373-381. doi: 10.4153/CMB-2018-013-x
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     author = {Loring, Terry A. and Schulz-Baldes, Hermann},
     title = {Spectral {Flow} {Argument} {Localizing} an {Odd} {Index} {Pairing}},
     journal = {Canadian mathematical bulletin},
     pages = {373--381},
     year = {2019},
     volume = {62},
     number = {2},
     doi = {10.4153/CMB-2018-013-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-013-x/}
}
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