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Conjugacy for positive permutation braids

Hugh R. Morton, Richard J. Hadji (2005)

Fundamenta Mathematicae

Positive permutation braids on n strings, which are defined to be positive n-braids where each pair of strings crosses at most once, form the elementary but non-trivial building blocks in many studies of conjugacy in the braid groups. We consider conjugacy among these elementary braids which close to knots, and show that those which close to the trivial knot or to the trefoil are all conjugate. All such n-braids with the maximum possible crossing number are also shown to be conjugate. ...

Conjugation spaces.

Hausmann, Jean-Claude, Holm, Tara, Puppe, Volker (2005)

Algebraic & Geometric Topology

Connected components of the strata of the moduli spaces of quadratic differentials

Erwan Lanneau (2008)

Annales scientifiques de l'École Normale Supérieure

In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...

Connections in regular Poisson manifolds over ℝ-Lie foliations

Jan Kubarski (2000)

Banach Center Publications

The subject of this paper is the notion of the connection in a regular Poisson manifold M, defined as a splitting of the Atiyah sequence of its Lie algebroid. In the case when the characteristic foliation F is an ℝ-Lie foliation, the fibre integral operator along the adjoint bundle is used to define the Euler class of the Poisson manifold M. When M is oriented 3-dimensional, the notion of the index of a local flat connection with singularities along a closed transversal is defined. If, additionally,...

Constructing equivariant maps for representations

Stefano Francaviglia (2009)

Annales de l’institut Fourier

We show that if Γ is a discrete subgroup of the group of the isometries of k , and if ρ is a representation of Γ into the group of the isometries of n , then any ρ -equivariant map F : k n extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable ρ -equivariant...

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