NKHYPORB · 2-generator discrete groups and hyperbolic orbifolds
6РП — Действия „Мария Кюри“
- Период
- 2004-12-01 → 2006-11-30
- Финансиране от ЕС
- 150 281 €
- Участници
- 1
- Схема
- IIF
Линиите свързват координатора с партньорите.
Накратко на български
Дискретните групи от два генератора и хиперболичните орбифолди се анализират чрез определяне на условията, при които тези групи съществуват. Това помага за точното описание на параметрите и геометрията на специфични пространства в теорията на Клейновите групи.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Final Activity Report Summary - NKHYPORB (2-generator Discrete Groups and Hyperbolic Orbifolds)
Discreteness criteria (necessary and sufficient conditions) are found for the non-elementary subgroups of PSL(2,C) without invariant plane in case when f is pi-loxodromic, g is parabolic or elliptic, and g has an invariant plane orthogonal to the axis of f. The orbifolds uniformised by such groups G are obtained, group presentations for G are found, and the trace parameters are computed. Since discreteness criteria are known for the subgroups of PSL(2,C) with a parabolic generator f and an elliptic, parabolic, or hyperbolic generator g, whose commutator has real trace, the result obtained has enabled us to describe all real points of the parameter space of two-generator Kleinian groups with a parabolic generator, that is to describe a certain two-dimensional slice through this space. In addition, a complete list of orbifolds uniformised by non-elementary two-generator subgroups of PSL(2,C) without invariant planes whose generators and their commutator have real traces is obtained.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
This project deals with the classification problem of 3-dimensional hyperbolic orbifolds or equivalently, the classification problem of discrete subgroups of PSL(2, C) which is isomorphic to the isometry group of the hyperbolic 3-dimensional space. We concentrate on 2-generator groups and orbifolds. The first part is dedicated to finding criteria (necessary and sufficient conditions) for discreteness of 2-generator subgroups of PSL(2,C) without invariant planes.The project is aimed to obtaining criteria that are convenient for different applications in algebra and topology. In the second part the aim is to describe all hyperbolic 3-orbifolds, i.e., to present their singular sets and the underlying spaces and to give conditions when such orbifolds exist. Another question arising here isto establish when an abstract group can be the fundamental group of a (hyperbolic) 3-orbifold. For example, hyperbolic 3-orbifolds are closely related to generalised triangle and tetrahedron groups. We plan to develop further connections between these objects.
Оригинален текст от CORDIS (на английски).
Участници
- CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE · PARISКоординаторФранция
Връзки
Данни: CORDIS, © Европейски съюз