NPC COMPLEXES · Non-positively curved complexes
6РП — Действия „Мария Кюри“
- Период
- 2007-10-01 → 2008-09-30
- Финансиране от ЕС
- 40 000 €
- Участници
- 1
- Схема
- ERG
Линиите свързват координатора с партньорите.
Накратко на български
Геометричната теория на групите изследва как определени математически структури действат върху клетъчни комплекси с неположителна кривина. Това помага за определянето на границите на тези групи и доказването на математически хипотези, като например конжектурата на Новиков.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Final Activity Report Summary - NPC COMPLEXES (Non-positively curved complexes)
The project concerns geometric group theory. We were studying group acting geometrically on cell complexes with various combinatorial non-positive curvatures-e.g. simplicial non-positive curvature (i.e. systolic groups) and CAT(0) cube complexes. In particular we were studying boundaries of such groups. The main outcomes of this fellowship are the two papers: [1] (with Piotr Przytycki) 'Boundaries of systolic groups', submitted. [2] 'On simplicial non-positive curvature', in preparation. In [1] we construct the boundary (in the sense of the Bestvina Z-structure) of systolic groups. Existence of such a boundary is conjectured for a large class of groups but up to now it is known only for few classes of groups. As a corollary we get e.g. the Novikov conjecture for torsion-free systolic groups. In [2] we introduce a new notion of a combinatorial non-positive curvature. This theory includes in particular systolic and CAT(0) cubical worlds. As an application we can extend some results obtained earlier for systolic groups. As for the training aspect of the project the most important was initiating of the regular studies in the domain of analysis on the boundaries of hyperbolic groups.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
The objective of this proposal is to study CAT(0) cube complexes and simplicially non-positively curved (SNPC) complexes, groups acting geometrically on them and relations between the two classes of spaces and groups. Part of the project is to study boundaries of the mentioned spaces and groups. This includes extending some results obtained by me earlier.I also plan to study the difference between groups acting geometrically on CAT(0) cube complexes and those acting on SNPC complexes. On the other hand, I will look for a theory unifying those two worlds. The host institution is Uniwersytet Wroclawski. I will be mainly working with Jacek Swiatkowski. We both have some experience in SNPC and I want to use the experience concerning CAT(0) cube complexes that I gained during my fellowship in Paris.Moreover, I will benefit a lot by working with other members of the geometric group theory team in Wroclaw which is the biggest one in Poland in the domain. I worked with some of them and I hope that the things I learned in Paris will help to increase the level of the group. One of the aims of this project is also developing the collaboration between the geometric group theory groups in Wroclaw and in Paris.Such a collaboration was started by Swiatkowski and Frederic Haglund (Orsay) and is still going on. In particular, I intend to continue our joint work with F. Haglund (Combinatorial cross-ratio on the boundary of CAT(0) cube complexes) that has begun during my fellowship in Paris. Moreover, the fellowship will prepare me excellently for a permanent academic position.
Оригинален текст от CORDIS (на английски).
Участници
- UNIWERSYTET WROCLAWSKI · WROCLAWКоординаторПолша
Връзки
Данни: CORDIS, © Европейски съюз