Thèse--Faculté des sciences de Paris, 1915.

Thèse--Faculté des sciences de Paris, 1915.

In this thesis we consider the group of fractional linear transformations of a variable x over an algebraically closed field k. The purpose of the thesis is to determine all finite subgroups of this group whose orders are not divisible by the characteristic of k. / Science, Faculty of / Mathematics, Department of / Graduate

The thesis deals with contact manifolds and their groups of transformations and relatedly with contact fibre bundles. We apply the framework of convenient calculus on in finite dimensional smooth manifolds to study the Chern-Weil theory of groups of strict contactomorphisms producing several non-vanishing type results on the cohomology of the classifying spaces of these groups. Moreover, we prove that the space of isocontact embeddings of one contact manifold to another can be given the structure of a smooth manifold and a principal bundle. Using this we describe a particular smooth model of the classifying space for the group Cont+(M; ) of (co-orientation preserving) contactomorphisms of a closed contact manifold (M; ). Lastly, we show that the standard action of the unitary group U(2) on the standard contact 3-sphere S3 induces a homotopy equivalence Cont+(S3; std) ' U(2).

No description available.

Thesis--Bonn. / Includes bibliographical references (p. 84).

Thesis--Bonn. / Includes bibliographical references (p. 84).

Revised version of the author's Ph. D. thesis, Free University, Amsterdam. / Includes bibliographical references (p. 236-245) and index.

This dissertation wants to understand the church history regarding the divide which resulted in the so called fundamentalist and the liberal movements in the church being birthed in identifying the reasons for the conflict between the aforementioned groups. It then presents principles of conflict transformation and management in order to understand and to help transform and manage potential confrontational situations between the aforementioned groups effectively. It further propose alternative interpretations to potential conflict-generating Bible texts by extrapolating new information from those texts in order to stir the potential of birthing a second naïve love for the discredited texts by offering new meanings to those same texts. Unfortunately, this objective can’t effectively be measured within the scope of this dissertation, but will nevertheless remain as an objective of hope.

Dans cette thèse, nous nous intéressons à diverses propriétés algébriques des groupes d'homéomorphismes et de difféomorphismes de variétés. On appelle fragmentation la possibilité d'écrire un homéomorphisme en tant que composé d'homéomorphismes supportés dans des boules. Tout d'abord, nous étudions la longueur des commutateurs sur le groupe des homéomorphismes du tore et de l'anneau, ainsi que la norme de fragmentation, qui associe à tout homéomorphisme le nombre minimal de facteurs nécessaires pour écrire cet homéomorphisme en tant que composé d'homéomorphismes supportés dans des boules. Dans une deuxième partie de la thèse, nous abordons una autre propriété algébrique des groupes d'homéomorphismes et de difféomorphismes : la distorsion. Celle-ci est reliée de manière surprenante à des propriétés de fragmentation des homéomorphismes. / In this thesis, we are interested in various algebraic properties of groups of homeomorphisms and diffeomorphisms of manifolds. We call fragmentation the possibility to write a homeomorphism as a composition of homeomorphisms supported in balls. First, we study the commutator length on the group of homeomorphisms of the torus and of the annulus, as well as the fragmentation norm, which associates to any homeomorphism the minimal number of factors necessary to write this homeomorphism as a composition of homeomorphisms supported in balls. In a second part of this thesis, we deal with another algebraic property of homeomorphism and diffeomorphism groups: the distortion. This last notion is surprisingly related to fragmentation properties of homeomorphisms.