112 research outputs found
The topology of a semisimple Lie group is essentially unique
We study locally compact group topologies on semisimple Lie groups. We show
that the Lie group topology on such a group is very rigid: every 'abstract'
isomorphism between and a locally compact and -compact group
is automatically a homeomorphism, provided that is absolutely
simple. If is complex, then non-continuous field automorphisms of the
complex numbers have to be considered, but that is all.Comment: To appear in: Advances in Mathematic
A Maslov cocycle for unitary groups
We introduce a 2-cocycle for symplectic and skew-hermitian hyperbolic groups
over arbitrary fields and skew fields, with values in the Witt group of
hermitian forms. This cocycle has good functorial properties: it is natural
under extension of scalars and stable, so it can be viewed as a universal
2-dimensional characteristic class for these groups. Over R and C, it coincides
with the first Chern class.Comment: To appear in Proc. London Math. So
Homogeneous compact geometries
We classify compact homogeneous geometries of irreducible spherical type and
rank at least 2 which admit a transitive action of a compact connected group,
up to equivariant 2-coverings. We apply our classification to polar actions on
compact symmetric spaces.Comment: To appear in: Transformation Group
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