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Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups

Assaf Libman (2011)

Fundamenta Mathematicae

Let G be a compact Lie group. We present a criterion for the orbit spaces of two G-spaces to be homotopy equivalent and use it to obtain a quick proof of Webb’s conjecture for compact Lie groups. We establish two Minami type formulae which present the p-localised spectrum Σ B G as an alternating sum of p-localised spectra Σ B H for subgroups H of G. The subgroups H are calculated from the collections of the non-trivial elementary abelian p-subgroups of G and the non-trivial p-radical subgroups of G. We...

Oscillating multipliers on the Heisenberg group

E. K. Narayanan, S. Thangavelu (2001)

Colloquium Mathematicae

Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator - 1 / 2 s i n is bounded on L p ( H ) for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on L p in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.

Parallélismes absolus des variétés lorentziennes

M. Cahen, M. Parker (1977)

Annales de l'institut Fourier

Tout parallélisme absolu d’une variété lorentzienne complète et simplement connexe respecte une décomposition de de Rham ; dans le cas faiblement irréductible mais non irréductible, la variété est un groupe de Lie résoluble.

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