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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Structurally stable Grassmann transformations


Author: Steve Batterson
Journal: Trans. Amer. Math. Soc. 231 (1977), 385-404
MSC: Primary 58F15
MathSciNet review: 0448443
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Abstract: A Grassmann transformation is a diffeomorphism on a Grassmann manifold which is induced by an $ n \times n$ nonsingular matrix. In this paper the structurally stable Grassmann transformations are characterized to be the maps which are induced by matrices whose eigenvalues have distinct moduli. There is exactly one topological conjugacy class of complex structurally stable Grassmann transformations. For the real case the topological classification is determined by the ordering (relative to modulus) of the signs of the eigenvalues of the inducing matrix.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0448443-6
PII: S 0002-9947(1977)0448443-6
Keywords: Grassmann manifold, Grassmann transformation, topological conjugacy, structurally stable, Morse-Smale, labelled diagram
Article copyright: © Copyright 1977 American Mathematical Society