61 research outputs found
The cohomology of exotic 2-local finite groups
There exist spaces BSol(q) which are the classifying spaces of a family of
2-local finite groups based on certain fusion system over the Sylow 2-subgroups
of Spin_7(q). In this paper we calculate the cohomology of BSol(q) as an
algebra over the Steenrod algebra A_2. We also provide the calculation of the
cohomology algebra over A_2 of the finite group of Lie type G_2(q).Comment: 13 page
The homotopy type of the complement of a coordinate subspace arrangement
The homotopy type of the complement of a complex coordinate subspace
arrangement is studied by fathoming out the connection between its topological
and combinatorial structures. A family of arrangements for which the complement
is homotopy equivalent to a wedge of spheres is described. One consequence is
an application in commutative algebra: certain local rings are proved to be
Golod, that is, all Massey products in their homology vanish.Comment: 42 page
The integral Pontrjagin homology of the based loop space on a flag manifold
The based loop space homology of a special family of homogeneous spaces, flag
manifolds of connected compact Lie groups is studied. First, the rational
homology of the based loop space on a complete flag manifold is calculated
together with its Pontrjagin structure. Second, it is shown that the integral
homology of the based loop space on a flag manifold is torsion free. This
results in a description of the integral homology. In addition, the integral
Pontrjagin structure is determined.Comment: revised version, 17 pages, to appear in Osaka Journal of Mathematic
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