On the linearity problem for mapping class groups.
On the linearization theorem for proper Lie groupoids
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout...
On the local isometric imbedding problem of 2-dimensional Riemannian manifolds in Euclidean space
On the Lusternik-Schnirelmann Category of Lie Groups.
On the Lusternik-Schnirelmann Category of Lie Groups: II.
On the Mahler measure of Jones polynomials under twisting.
On the Malcev completion of Kähler groups.
On the Margulis constant for Kleinian groups. I.
On the meaning of Bell's inequalities violation
On the Milnor fibrations of weighted homogeneous polynomials
On the minimizers of the Möbius cross energy of links.
On the mod p Betti numbers of loop spaces.
On the Mod p Torus Theorem of John Hubbuck.
On the Morse Complex.
On the Nature of Thin Complements of Complete Kähler Metrics.
On the non-existence of certain group topologies
Minimal Hausdorff (Baire) group topologies of certain groups of transformations naturally occurring in analysis are studied. The results obtained are subsequently applied to show that, e.g., the homeomorphism groups of the rational and of the irrational numbers carry no Polish group topology. In answer to a question of A. S. Kechris it is shown that the group of Borel automorphisms of ℝ cannot be a Polish group either.
On the non-invariance of span and immersion co-dimension for manifolds
In this note we give examples in every dimension of piecewise linearly homeomorphic, closed, connected, smooth -manifolds which admit two smoothness structures with differing spans, stable spans, and immersion co-dimensions. In dimension the examples include the total spaces of certain -sphere bundles over . The construction of such manifolds is based on the topological variance of the second Pontrjagin class: a fact which goes back to Milnor and which was used by Roitberg to give examples...
On the Novikov complex for rational Morse forms
On the number of components of the symplectic representatives of the canonical class
We show that there exists a family of simply connected, symplectic 4-manifolds such that the (Poincaré dual of the) canonical class admits both connected and disconnected symplectic representatives. This answers a question raised by Fintushel and Stern.
On the number of non-equivalent differentiable structures on 4-Manifolds.