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Spaces of Hermitian Operators with Simple Spectra and their Finite-Order Cohomology

2003
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Moscow Mathematical Journal
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V. I. Arnold studied the topology of spaces of Hermitian operators with non-simple spectra in C n in relation to the theory of adiabatic connections and the quantum Hall effect. (Important physical motivations of this problem were also suggested by S. P. Novikov.) The natural stratification of these spaces into the sets of operators with fixed numbers of eigenvalues defines a spectral sequence providing interesting combinatorial and homological information on this stratification. We construct a

doi:10.17323/1609-4514-2003-3-3-1145-1165
fatcat:ufpvtiqkr5hdrjqmo3nkzb7tfu