Manifolds which admit actions
Maximal Hamiltonian tori for polygon spaces
We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.
Measured foliations and mapping class groups of surfaces.
Measure-preserving homeomorphisms of noncompact manifolds and mass flow toward ends
Suppose M is a noncompact connected n-manifold and ω is a good Radon measure of M with ω(∂M) = 0. Let ℋ(M,ω) denote the group of ω-preserving homeomorphisms of M equipped with the compact-open topology, and the subgroup consisting of all h ∈ ℋ(M,ω) which fix the ends of M. S. R. Alpern and V. S. Prasad introduced the topological vector space (M,ω) of end charges of M and the end charge homomorphism , which measures for each the mass flow toward ends induced by h. We show that the map has...
Metric rigidity of crystallographic groups.
Minimal dimensions for flat manifolds with prescribed holonomy.
Minimality and unique ergodicity for subgroup actions
Let be an -algebraic semisimple group, an algebraic -subgroup, and a lattice in . Partially answering a question posed by Hillel Furstenberg in 1972, we prove that if the action of on is minimal, then it is uniquely ergodic. Our proof uses in an essential way Marina Ratner’s classification of probability measures on invariant under unipotent elements, and the study of “tubes” in .
Mod 2 Semi-characteristics and the Converse to a Theorem of Milnor.
Modular circle quotients and PL limit sets.
Moment-angle complexes from simplicial posets
We extend the construction of moment-angle complexes to simplicial posets by associating a certain T m-space Z S to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤ[S] by topological methods. The space Z S has many important topological properties of the original moment-angle complex Z K associated to...
Monoids on the 2-disk.
Multicontact vector fields on Hessenberg manifolds.