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The Dehn functions of O u t ( F n ) and A u t ( F n )

Martin R. Bridson, Karen Vogtmann (2012)

Annales de l’institut Fourier

For n at least 3, the Dehn functions of O u t ( F n ) and A u t ( F n ) are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case n = 3 was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for n bigger than 3 to the case n = 3 . In this note we give a shorter, more direct proof of this last reduction.

The Equivariant Bundle Subtraction Theorem and its applications

Masaharu Morimoto, Krzysztof Pawałowski (1999)

Fundamenta Mathematicae

In the theory of transformation groups, it is important to know what kind of isotropy subgroups of G do occur at points of the space upon which the given group G acts. In this article, for a finite group G, we prove the Equivariant Bundle Subtraction Theorem (Theorem 2.2) which allows us to construct smooth G-manifolds with prescribed isotropy subgroups around the G-fixed point sets. In Theorem 0.1, we restate Oliver's result about manifolds M and G-vector bundles over M that occur, respectively,...

The hyperKähler geometry associated to Wolf spaces

Piotr Kobak, Andrew Swann (2001)

Bollettino dell'Unione Matematica Italiana

Sia G un grupo di Lie compatto e semplice. Sia O min la più piccola orbita nilpotente non-banale nell'algebra di Lie complessa g C . Si presenta una costruzione diretta di teoria di Lie delle metriche iperKahler su O min con potenziale Kahleriano G -invariante e compatibili con la forma simplettica complessa di Kostant-Kirillov-Souriau. In particolare si ottengono le metriche iperKahler dei fibrati associati sugli spazi di Wolf (spazi simmetrici quaternionali a curvatura scalare positiva).

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