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The goal of this course/seminar is to introduce the students to some contemporary aspects of geometric group theory. Emphasis will be put on Artin's Braid groups and Thompson's groups.
In the mathematical field of topology, a homeomorphism (, named by Henri Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the —that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Given two manifolds and , a differentiable map is called a diffeomorphism if it is a bijection and its inverse is differentiable as well. If these functions are times continuously differentiable, is called a -diffeomorphism. Two manifolds and are diffeomorphic (usually denoted ) if there is a diffeomorphism from to .
In mathematics, a free abelian group is an abelian group with a basis. Being an abelian group means that it is a set with an addition operation that is associative, commutative, and invertible. A basis, also called an integral basis, is a subset such that every element of the group can be uniquely expressed as an integer combination of finitely many basis elements. For instance the two-dimensional integer lattice forms a free abelian group, with coordinatewise addition as its operation, and with the two points (1,0) and (0,1) as its basis.
We show that for a large class C of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group G of rank k in C, there is a sequence of k-m
2020
We show that the finitely generated simple left orderable groups G(rho) constructed by the first two authors in Hyde and Lodha [Finitely generated infinite simple groups of homeomorphisms of the real
We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical typ