On the space of symmetric operators with multiple ground states
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We study the homology structure of the filtration of the space of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting on a finite-dimensional complex or real Hilbert space, but infinite-dimensional generalizations are easy to guess.
Key wordsself-adjoint operator multiple eigenvalue exact sequence
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- V. I. Arnold, “Modes and quasimodes,” Funkts. Anal. Prilozhen., 6:2 (1972), 12–20; English transl.: Functional Anal. Appl., 6:2 (1972), 94–101.Google Scholar