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Spectral Flow Argument Localizing an Odd Index Pairing

  • Terry A. Loring (a1) and Hermann Schulz-Baldes (a2)

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.

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The authors thank the Simons Foundation (CGM 419432), the NSF (DMS 1700102), and the DFG (SCHU 1358/3-4) for financial support.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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