FP6Индивидуална стипендия2006–2008

AYCRM · Characterisations of geometric groups

6РП — Действия „Мария Кюри“

Период: 2006-12-01 → 2008-11-30
Финансиране от ЕС: 130 211 €
Участници: 1
Схема: EIF

Линиите свързват координатора с партньорите. За проекти отпреди 2014 г. CORDIS не винаги дава точни координати. Тези точки са на ниво град или държава.

Накратко на български

Геометричната теория на групите изследва връзката между алгебрата и геометрията, като например как свойствата на хиперболичните групи описват пространството, в което те действат. Тази кореспонденция помага да се разберат топологичните и геометричните характеристики на тези пространства.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Final Activity Report Summary - AYCRM (Characterisations of geometric groups)

I worked on hyperbolic groups, more generally on geometric group theory. Around 1970's hyperbolic geometry and group theory has interacted profoundly creating a very waste intersection area. When a group acts naturally on a geometric space, one can use the geometric information to define and study the group, and inversely the algebraic information on the group may induce strong result on the topology and geometry of the space on which a group acts naturally. This essential correspondence gave rise at notion of hyperbolic groups. These groups are now known to be to generic example of the geometric groups.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

Results involving all finitely generated groups are often of very little interest, and therefore combinatorial group theory concentrates on particular classes of groups. Hyperbolic groups form one of the classes that offer an extremely satisfactory compromise between interest and generality, as one can prove very precise structural results for such groups. In our project we propose to work on relatively hyperbolic groups, which are a generalisation of hyperbolic groups, and on some other questions involving the techniques and methods of the related theories. There are already several characterisations of relatively hyperbolic groups from different points of view, like dynamical or topological. One of the problems that we propose here is to give a cohomological characterisation of relatively hyperbolic groups, namely to study the relative bounded cohomology and to understand the connection between bounded cohomology and standard cohomology. Another problem we would like to work on involves relative metabolicity. It has been proved that relative metabolicity implies weak relative hyperbolicity. It would be an attractive result to strengthen this result, and to show that relative metabolicity actually implies relative hyperbolicity in the strong sense. The third problem is a natural continuation of an earlier work, and aims to find out which classes of finitely generated groups satisfy the property of special symbol". This property was introduced in order to encode the action of relatively hyperbolic groups on their boundaries by means of symbolic dynamics. Finally, I would like to weaken the hypotheses of a recent result on configuration spaces and cocompact properly discontinuous group actions. This question and the methods to approach it involve the techniques that were used to give a dynamical characterisation of relatively hyperbolic groups. If the hypotheses are formulated in their greatest generality, this will be an attra"

Оригинален текст от CORDIS (на английски).

Участници

CENTRE DE RECERCA MATEMATICA · BELLATERRAКоординаторНиво градИспания

Връзки

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