1,720,962 research outputs found
On the Kropholler conjecture
No full textThis short note, produced for the volume of conjectures produced on the occasion of Guido Mislin's retirement, describes the status of the Kropholle conjecture which may be viewed as a far reaching generalisation of Stallings' theorem on groups with more than one end
Minimal cubings
Full text linkWe combine ideas of Scott and Swarup on good position for almost invariant subsets of a group with ideas of Sageev on constructing cubings from such sets. We construct cubings which are more canonical than in Sageev's original construction. We also show that almost invariant sets can be chosen to be in very good position
Codimension-1 Subgroups and Splittings of Groups
No full textAbstractWe show that under certain circumstances, a codimension-1 subgroupHof a finitely generated groupGeither provides a splitting ofGas an amalgam or provides a codimension-1 subgroup ofH. In particular, ifGis hyperbolic andHis quasiconvex, one gets a descending sequence of codimension-1 subgroups, terminating at a splitting. In the process, we settle a conjecture of Kropholler and Roller for the case of quasiconvex subgroups of hyperbolic groups
Coarse cubical rigidity
Full text linkWe show that for many right-angled Artin and Coxeter groups, all cocompact cubulations coarsely look the same: they induce the same coarse median structure on the group. These are the first examples of non-hyperbolic groups with this property.
For all graph products of finite groups and for Coxeter groups with no irreducible affine parabolic subgroups of rank , we show that all automorphism preserve the coarse median structure induced, respectively, by the Davis complex and the Niblo-Reeves cubulation. As a consequence, automorphisms of these groups have nice fixed subgroups and satisfy Nielsen realisation.42 pages, 7 figures; to appear in Journal of Topolog
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Geometric group theory
No full textGeometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory
Cubulating Surface-by-free Groups
Full text linkLet be an exact sequence where is the fundamental group of a closed surface of genus greater than one, is hyperbolic and is finitely generated free. The aim of this paper is to provide sufficient conditions to prove that is cubulable and construct examples satisfying these conditions. The main result may be thought of as a combination theorem for virtually special hyperbolic groups when the amalgamating subgroup is not quasiconvex. Ingredients include the theory of tracks, the quasiconvex hierarchy theorem of Wise, the distance estimates in the mapping class group from subsurface projections due to Masur-Minsky and the model geometry for doubly degenerate Kleinian surface groups used in the proof of the ending lamination theorem.
An appendix to this paper by Manning, Mj, and Sageev proves a reduction theorem by showing that cubulability of follows from the existence of an essential incompressible quasiconvex track in a surface bundle over a graph with fundamental group .v2: major revision. 64 pages, 5 figures. The main body of the paper is now by Mj, with an appendix by Manning, Mj, and Sageev v3: Final version. 65 pages, 5 figures. To appear in Journal of Topolog
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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