Simplicial and categorical diagrams, and their equivariant applications.
Simplicial groups as models for -types
Simplicial matrices and the nerves of weak -categories I: Nerves of bicategories.
Smooth Compact Lie Group Actions on Disks.
Some geometric perspectives in concurrency theory.
Spaces associated to quadratic endofunctors of the category of groups.
Square groups are gadgets classifying quadratic endofunctors of the category of groups. Applying such a functor to the Kan simplicial loop group of the 2-dimensional sphere, one obtains a one-connected three-type. We consider the problem of characterization of those three-types X which can be obtained in this way. We solve this problem in some cases, including the case when π2(X) is a finitely generated abelian group. The corresponding stable problem is solved completely.
Spaces of polynomials with roots of bounded multiplicity
We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.
Steenrod's Equivariant Moore Space Problem for Cohomologically Trivial Modules.
Suites inertes dans les algèbres de Lie grasuées. ("Autopsie d'un meurtre II").
Sur le type d'homotopie d'un CW-complexe.
Symplectic groups are N-determined 2-compact groups
We show that for n ≥ 3 the symplectic group Sp(n) is as a 2-compact group determined up to isomorphism by the isomorphism type of its maximal torus normalizer. This allows us to determine the integral homotopy type of Sp(n) among connected finite loop spaces with maximal torus.