3,396 research outputs found
On fixed point sets of distinguished collections for groups of parabolic characteristic
We determine the nature of the fixed point sets of groups of order p, acting
on complexes of distinguished p-subgroups (those p-subgroups containing
p-central elements in their centers). The case when G has parabolic
characteristic p is analyzed in detail.Comment: 15 page
The topology of deformation spaces of Kleinian groups
Let M be a compact, hyperbolizable 3-manifold with nonempty incompressible
boundary and let AH(\pi_1(M)) denote the space of (conjugacy classes of)
discrete faithful representations of \pi_1(M) into PSL 2 (C). The components of
the interior MP(\pi_1(M)) of AH(\pi_1(M)) (as a subset of the appropriate
representation variety) are enumerated by the space A(M) of marked
homeomorphism types of oriented, compact, irreducible 3-manifolds homotopy
equivalent to M. In this paper, we give a topological enumeration of the
components of the closure of MP(\pi_1(M)) and hence a conjectural topological
enumeration of the components of AH(\pi_1(M)). We do so by characterizing
exactly which changes of marked homeomorphism type can occur in the algebraic
limit of a sequence of isomorphic freely indecomposable Kleinian groups. We use
this enumeration to exhibit manifolds M for which AH(\pi_1(M)) has infinitely
many components.Comment: 49 pages, published versio
On a homotopy relation between the 2-local geometry and the Bouc complex for the sporadic group Co3
We study the homotopy relation between the standard 2-local geometry and the
Bouc complex for the sporadic group Co3. We also give a result concerning the
relative projectivity of the reduced Lefschetz module associated to the
aformentioned 2-local geometry.Comment: 20 page
New collections of p-subgroups and homology decompositions for classifying spaces of finite groups
Let G be a finite group and p a prime dividing its order. We define new
collections of p-subgroups of G. We study the homotopy relations among them and
with the standard collections of p-subgroups. We determine their ampleness and
sharpness properties.Comment: 14 pages, some revisions made, final version to appear in
Communications in Algebr
On fixed point sets and Lefschetz modules for sporadic simple groups
We consider 2-local geometries and other subgroup complexes for sporadic
simple groups. For six groups, the fixed point set of a noncentral involution
is shown to be equivariantly homotopy equivalent to a standard geometry for the
component of the centralizer. For odd primes, fixed point sets are computed for
sporadic groups having an extraspecial Sylow p-subgroup of order p^3, acting on
the complex of those p-radical subgroups containing a p-central element in
their centers. Vertices for summands of the associated reduced Lefschetz
modules are described.Comment: 22 page
Degenerate flag varieties: moment graphs and Schr\"oder numbers
We study geometric and combinatorial properties of the degenerate flag
varieties of type A. These varieties are acted upon by the automorphism group
of a certain representation of a type A quiver, containing a maximal torus T.
Using the group action, we describe the moment graphs, encoding the zero- and
one-dimensional T-orbits. We also study the smooth and singular loci of the
degenerate flag varieties. We show that the Euler characteristic of the smooth
locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is
given by a natural statistics counting the number of diagonal steps in a
Schr\"oder path. As an application we obtain a new combinatorial description of
the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page
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