Spectral flows of dilations of Fredholm operators

Abstract

Given an essentially unitary contraction and an arbitrary unitary dilation of it, there is a naturally associated spectral flow which is shown to be equal to the index of the operator. This purely operator theoretic result is interpreted in terms of the $K$-theory of an associated mapping cone. It is then extended to connect $Z_2$ indices of odd symmetric Fredholm operators to a $Z_2$-valued spectral flow.

final version, to appear in Cand. Math. Bull

References in corpus (3)

• Spectral flows associated to flux tubes
• Z_2 indices and factorization properties of odd symmetric Fredholm operators
• A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory

Cited by in corpus (10)

• Spectral flows associated to flux tubes
• Chern numbers as half-signature of the spectral localizer
• Rational indices for quantum ground state sectors
• The FKMM-invariant in low dimension
• Bulk-edge correspondence and the cobordism invariance of the index
• A many-body Fredholm index for ground state spaces and Abelian anyons
• Parity flow as ${\mathbb{Z}}_2$-valued spectral flow
• Classification of topological invariants related to corner states
• The cohomology invariant for class DIII topological insulators
• Skew localizer and ${\mathbb{Z}}_2$-flows for real index pairings