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Bounded cohomology of lattices in higher rank Lie groups

Marc Burger, Nicolas Monod (1999)

Journal of the European Mathematical Society

We prove that the natural map H b 2 ( Γ ) → H 2 ( Γ ) from bounded to usual cohomology is injective if Γ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for Γ : the stable commutator length vanishes and any C 1 –action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating H * b ( Γ ) to the continuous bounded cohomology of the ambient group...

Bounds for Chern classes of semistable vector bundles on complex projective spaces

Wiera Dobrowolska (1993)

Colloquium Mathematicae

This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on ℙ n . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on ℙ 4 and a generalization of the presented method to r-bundles on ℙ n is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.

Bouquets of circles for lamination languages and complexities

Philippe Narbel (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Laminations are classic sets of disjoint and non-self-crossing curves on surfaces. Lamination languages are languages of two-way infinite words which code laminations by using associated labeled embedded graphs, and which are subshifts. Here, we characterize the possible exact affine factor complexities of these languages through bouquets of circles, i.e. graphs made of one vertex, as representative coding graphs. We also show how to build families of laminations together with corresponding lamination...

Bouts d'un groupe opérant sur la droite, I : théorie algébrique

Gaël-Nicolas Meigniez (1990)

Annales de l'institut Fourier

On étudie les morphismes d’un groupe infini discret Π dans un groupe de Lie G contenu dans le groupe des difféomorphismes de la droite réelle. À un tel morphisme H , on associe deux ensembles de “bouts” de Π “dans la direction” H . On calcule le nombre de bouts dans plusieurs situations. Dans le cas particulier où Π est de type fini et où G est le groupe des translations, Π n’a qu’un bout dans la direction H si, et seulement si, ils vérifient la propriété de Bieri-Neumann-Strebel.

Braid Monodromy of Algebraic Curves

José Ignacio Cogolludo-Agustín (2011)

Annales mathématiques Blaise Pascal

These are the notes from a one-week course on Braid Monodromy of Algebraic Curves given at the Université de Pau et des Pays de l’Adour during the Première Ecole Franco-Espagnole: Groupes de tresses et topologie en petite dimension in October 2009.This is intended to be an introductory survey through which we hope we can briefly outline the power of the concept monodromy as a common area for group theory, algebraic geometry, and topology of projective curves.The main classical results are stated...

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