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Generalized symmetric spaces and minimal models

Anna Dumańska-Małyszko, Zofia Stępień, Aleksy Tralle (1996)

Annales Polonici Mathematici

We prove that any compact simply connected manifold carrying a structure of Riemannian 3- or 4-symmetric space is formal in the sense of Sullivan. This result generalizes Sullivan's classical theorem on the formality of symmetric spaces, but the proof is of a different nature, since for generalized symmetric spaces techniques based on the Hodge theory do not work. We use the Thomas theory of minimal models of fibrations and the classification of 3- and 4-symmetric spaces.

Genus sets and SNT sets of certain connective covering spaces

Huale Huang, Joseph Roitberg (2007)

Fundamenta Mathematicae

We study the genus and SNT sets of connective covering spaces of familiar finite CW-complexes, both of rationally elliptic type (e.g. quaternionic projective spaces) and of rationally hyperbolic type (e.g. one-point union of a pair of spheres). In connection with the latter situation, we are led to an independently interesting question in group theory: if f is a homomorphism from Gl(ν,A) to Gl(n,A), ν < n, A = ℤ, resp. ℤ p , does the image of f have infinite, resp. uncountably infinite, index in...

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