Jan Essert
Homological stability for classical groups.
Ср, 10/14/2009 - 11:03 — SomNambulAuthors: Jan Essert
Subjects: K-Theory and Homology
AbstractAssociated to every group with a weak spherical BN pair of rank n+1 with an
appropriate rank n subgroup, we construct a relative spectral sequence
involving group homology of Levi subgroups of both groups. Using the fact that
such Levi subgroups frequently split as semidirect products of smaller groups,
we prove homological stability results for unitary groups over division rings
with infinite centre as well as for special linear and special orthogonal
groups over infinite fields.- 1 комментарий
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Homological stability for classical groups.
Ср, 10/14/2009 - 11:03 — SomNambulAuthors: Jan Essert
Subjects: K-Theory and Homology
AbstractAssociated to every group with a weak spherical BN pair of rank n+1 with an
appropriate rank n subgroup, we construct a relative spectral sequence
involving group homology of Levi subgroups of both groups. Using the fact that
such Levi subgroups frequently split as semidirect products of smaller groups,
we prove homological stability results for unitary groups over division rings
with infinite centre as well as for special linear and special orthogonal
groups over infinite fields.A geometric construction of panel-regular lattices in buildings of types ~A_2 and ~C_2.
Чт, 08/20/2009 - 23:06 — SomNambulAuthors: Jan Essert
Subjects: Group Theory
AbstractUsing Singer polygons, we construct locally finite affine buildings of types
~A_2 and ~C_2 which admit uniform lattices acting regularly on panels. This
construction produces very explicit descriptions of these buildings as well as
very short presentations of the lattices. All but one of the ~C_2-buildings are
necessarily exotic. Integral and rational group homology for the lattices is
also calculated.
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