The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers; specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the Beltrami equation has deep implications for the theory of Kleinian groups and their deformations.
This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space.
This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.
Assuming only basic algebra and Galois theory, the book develops the method of "e;algebraic patching"e; to realize finite groups and, more generally, to solve finite split embedding problems over fields.
One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram.
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus.
The 2-volume-book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research.
The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research.
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction.
From 1-4 April 1986 a Symposium on Algebraic Groups was held at the University of Utrecht, The Netherlands, in celebration of the 350th birthday of the University and the 60th of T.
This book reviews recent results on low-dimensional quantumfield theories and their connection with quantum grouptheory and the theory of braided, balanced tensorcategories.
Gromov's theory of hyperbolic groups have had a big impactin combinatorial group theory and has deep connections withmany branches of mathematics suchdifferential geometry,representation theory, ergodic theory and dynamical systems.
The scope of the Israel seminar in geometric aspects of functional analysis during the academic year 89/90 was particularly wide covering topics as diverse as: Dynamical systems, Quantum chaos, Convex sets in Rn, Harmonic analysis and Banach space theory.
In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces.
This monograph addresses the problem of describing allprimitive soluble permutation groups of a given degree, withparticular reference to those degrees less than 256.
This book surveys the recent theory of wavelet transforms and its applications in various fields both within mathematics (singular integrals, localization of singularities) and beyond it, in computer vision, the physics of fractals, time-frequency analysis.
This research monograph provides a self-contained approach to the problem of determining the conditions under which a compact bordered Klein surface S and a finite group G exist, such that G acts as a group of automorphisms in S.
The problem of determining which S-arithmetic groups have a finite presentation is solved for arbitrary linear algebraic groups over finite extension fields of #3.
