We study the topology of moduli spaces of polygons with xed side lengths in the Euclidean plane. We establish a duality between the spaces of marked Euclidean polygons with xed side lengths andâ€¦ (More)

We study the symplectic geometry of moduli spaces M r of polygons with xed side lengths in Euclidean space. We show that M r has a natural structure of a complex analytic space and isâ€¦ (More)

We prove that for any affine variety S defined over Q there exist Shephard and Artin groups G such that a Zariski open subset U of S is biregular isomorphic to a Zariski open subset of the characterâ€¦ (More)

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n âˆ’ 1)â€¦ (More)

We give a lower bound to the dimension of a contractible manifold on which a given group can act properly discontinuously. In particular, we show that the n-fold product of nonabelian free groupsâ€¦ (More)

â€“ If a torsion-free hyperbolic group G has 1-dimensional boundary âˆ‚âˆžG, then âˆ‚âˆžG is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When âˆ‚âˆžG is a Sierpinski carpetâ€¦ (More)

We prove quasi-isometry invariance of the canonical decomposition for fundamental groups of Haken 3-manifolds with zero Euler characteristic. We show that groups quasi-isometric to Haken manifoldâ€¦ (More)

We prove realizability theorems for vector-valued polynomial mappings, real-algebraic sets and compact smooth manifolds by moduli spaces of planar linkages. We also establish a relation betweenâ€¦ (More)

We prove that the fundamental group of any compact Haken manifold of zero Euler characteristic, which is neither Nil nor Sol, is nonpositvely curved on the large scale.