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Orthogonal transformations for which topological equivalence implies linear equivalence

1982
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Bulletin of the American Mathematical Society
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Let R t , R 2 £ 0(ri) 9 the group of orthogonal transformations of R". We say R t and R 2 are topologically (resp. linearly) equivalent if there is a homeomorphism (resp. linear automorphism) ƒ: R n -• R n such that (Of course, linear equivalence of R t with R 2 is the same as equality of the respective sets of complex eigenvalues.) The order of an orthogonal transformation is its order as an element of 0(n). The purpose of this note is to announce and discuss the proof of the following result

doi:10.1090/s0273-0979-1982-15016-9
fatcat:e5cxvkqbcrgvhlhcjln45xxnya