163 Result(s)
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Open AccessThe strong Novikov conjecture for low degree cohomology
We show that for each discrete group Γ, the rational assembly map $$K_*(B\Gamma) \otimes {\mathbb{Q}} \to K_*(C^*_{\max}\Gamma) \otimes {\math...
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Open AccessEquivariant plateau problems
Let (M, Q) be a compact, three dimensional manifold of strictly negative sectional curvature. Let (Σ, P) be a compact, orientable surface of hyperbolic type (i.e. of genus at least two). Let θ : π1(Σ, P) → π1(M,
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Open AccessL’application cotangente des surfaces de type général
We study surfaces of general type S whose cotangent sheaf is generated by its global sections. We define a map called the cotangent map of S that enables us to understand the obstructions to the ampleness of the ...
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Open AccessKnots and k-width
We investigate several natural invariants of curves and knots in \({\mathbb{R}^3}\) . These invariants generalize bridge number...
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Open AccessInfinite genus surfaces and irrational polygonal billiards
We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus topological ...
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Open AccessA family of non-isomorphism results
We calculate the local groups of germs associated with the higher dimensional R. Thompson groups nV. For a given $${n\in N\cup\left\{\...
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Open AccessPerelman’s \({\bar{\lambda}}\) -invariant and collapsing via geometric characteristic splittings
Any closed, orientable, smooth, nonpositively curved manifold M is known to admit a geometric characteristic splitting, analogous to the JSJ decomposition in three dimensions. We show that when this splitting con...
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Open AccessLimits of dihedral groups
We characterise limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of genera...
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Open AccessFord fundamental domains in symmetric spaces of rank one
We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the c...
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Open AccessBlocks of monodromy groups in complex dynamics
Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including ...
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Open AccessRuled quartic surfaces, models and classification
New historical aspects of the classification, by Cayley and Cremona, of ruled quartic surfaces and the relation to string models and plaster models are presented. In a ‘modern’ treatment of the classification ...
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Open AccessSpherical complexes attached to symplectic lattices
To the integral symplectic group \({{\rm Sp}(2g,\mathbb{Z})}\) we associate two posets of which we prove that they ha...
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Open AccessConformality of a differential with respect to Cheeger-Gromoll type metrics
We investigate conformality of the differential of a map** between Riemannian manifolds if the tangent bundles are equipped with a generalized metric of Cheeger-Gromoll type.
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Open AccessInsecurity for compact surfaces of positive genus: commentary
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Open AccessCrosscap slides and the level 2 map** class group of a nonorientable surface
Crosscap slide is a homeomorphism of a nonorientable surface of genus at least 2, which was introduced under the name Y-homeomorphism by Lickorish as an example of an element of the map** class group which c...
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Open AccessAsymptotic dimension and small subsets in locally compact topological groups
We prove that for a coarse space \(X\) the ideal ...
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Open AccessA Lefschetz duality for intersection homology
We prove a Lefschetz duality theorem for intersection homology. Usually, this result applies to pseudomanifolds with boundary which are assumed to have a “collared neighborhood of their boundary”. Our duality ...
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Open AccessSingularities of equidistants and global centre symmetry sets of Lagrangian submanifolds
We study the global centre symmetry set (GCS) of a smooth closed submanifold \(M^m\subset \mathbb{R }^n, n \le 2m\) . ...
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Open AccessGeneralized symplectic symmetric spaces
Bieliavsky introduced and investigated a class of symplectic symmetric spaces, that is, symmetric spaces endowed with a symplectic structure invariant with respect to symmetries. The theory of symmetric spaces...
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Open AccessInvariance of finiteness of K-area under surgery
K-area is an invariant for Riemannian manifolds introduced by Gromov as an obstruction to the existence of positive scalar curvature. However in general it is difficult to determine whether K-area is finite or...