Open 3-manifolds and branched coverings: a quick exposition.
Open 3-manifolds, wild subsets of S3 and branched coverings.
In this paper, a representation of closed 3-manifolds as branched coverings of the 3-sphere, proved in [13], and showing a relationship between open 3-manifolds and wild knots and arcs will be illustrated by examples. It will be shown that there exist a 3-fold simple covering p : S3 --> S3 branched over the remarkable simple closed curve of Fox [4] (a wild knot). Moves are defined such that when applied to a branching set, the corresponding covering manifold remains unchanged, while the branching...
Open books and configurations of symplectic surfaces.
Open Subsets of LF-spaces
Let F = ind lim Fₙ be an infinite-dimensional LF-space with density dens F = τ ( ≥ ℵ ₀) such that some Fₙ is infinite-dimensional and dens Fₙ = τ. It is proved that every open subset of F is homeomorphic to the product of an ℓ₂(τ)-manifold and (hence the product of an open subset of ℓ₂(τ) and ). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.
Orbit spaces of the hyperspace of a graph which are Hilbert cubes
Order of holonomy and geometric objects of manifolds with connection
Orientability of total spaces of fibre bundles over
Orientation Reversing Involutions and the First Betti Number for Finite Coverings of 3-Manifolds.
Orientation Reversing Morse-Smale Diffeomorphisms of S2.
Orientation-reversing homeomorphisms in surface geography.
Ozsváth-Szabó invariants and tight contact three-manifolds; I.
Pachner move and affine volume-preserving geometry in .
Pappus's theorem and the modular group
Perfect stratifications and theory of weights.
In this paper we emphasize Deligne's theory of weights, in order to prove that some stratifications of algebraic varieties are perfect. In particular, we study in some detail the Bialynicki-Birula's stratifications and the stratifications considered by F. Kirwan to compute the cohomology of symplectic or geometric quotients. Finally we also appoint the motivic formulation of this approach, which contains the Hodge theoretic formulation.
Periodic actions on (I-D) normed linear spaces
Periodic actions on the Hilbert cube
Periodic homeomorphisms on and cubes with torus knotted holes
Periodicity of Branched Cyclic Covers of Manifolds with Open Book Decomposition.
Peripheral separability and cusps of arithmetic hyperbolic orbifolds.
Peripheral Structure of 3-Manifolds