A Topological Approach To Spectral Flow

Author: Yohei Tanaka

Tanaka, Yohei, 2014 A Topological Approach To Spectral Flow, Flinders University, School of Computer Science, Engineering and Mathematics

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Abstract

It is a well-known result of T. Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result, which naturally arises in the context of unitary spectral flow. This provides a new approach to spectral flow, which seems to be missing from the literature. It is the purpose of this paper to fill in this gap.

Keywords: continuous enumeration,spectral flow
Subject: Mathematics thesis

Thesis type: Masters
Completed: 2014
School: School of Computer Science, Engineering and Mathematics
Supervisor: Dr Nurulla Azamov