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The Mathematical Legacy of Wilhelm Magnus.
Wilhelm Magnus was an extraordinarily creative mathematician who made fundamental contributions to diverse areas, including group theory, geometry, and special functions. This book contains the proceedings of a conference held in May 1992 at Polytechnic University to honor the memory of Magnus. The...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
1994.
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| Colección: | Contemporary Mathematics Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Contents; Preface; Inequalities for plane quasiconformal mappings; A look at the Bateman project; Linear-central filtrations on groups; Musings on Magnus; The monodromy group of a transcendental function; Finite-dimensional representations of Artin's braid group; Squaring rectangles: The finite Riemann mapping theorem; 0. Introduction.; 1. Squared rectangles.; 1.1. Scientific American.; 1.2. Resistive circuits and the laws of Ohm and Kirchhoff.; 1.3. The solution of the resistive circuit problem.; 1.4. Planar circuits and rectangles tiled by rectangles.; 1.5. Max Dehn's contribution.
- 2. Optimal weight functions. 2.1. The classical Riemann mapping theorem.; 2.2. The finite problem and the existence and uniqueness of its solution.; 2.3. The geometry of an optimal weight function: general results.; 2.4. The geometry of an optimal weight function: special results for quadrilaterals and rings.; 3. The finite Riemann mapping theorem.; 3.1. Examples.; 3.2. The Kirchhoff inequalities.; 4. Algorithms which calculate the finite Riemann mapping.; 4.1. The minimal path algorithm.; 4.2. Proofs of the claims about the minimal path algorithm.
- 4.3. The efficiency of the minimal path algorithm. 4.4. Flow diagrams and a hybrid algorithm for the finite Riemann mapping problem.; 4.5. An example of the effectiveness of the hybrid algorithm.; 5. Optimal weight functions for 2-layer valence 3 tilings of quadrilaterals.; 5.1. Basic definitions and properties.; 5.2. Unique prime factorization theorem.; 5.3. Prime tilings.; 5.4. Preparations for factorization algorithms.; 5.5. The left factor algorithm.; 5.6. The joint ratio algorithm.; 6. Approximating combinatorial moduli.; 6.1. Skinny approximation.; 6.2. The averaging trick.
- 6.3. Examples. 7. Variable negative curvature versus constant curvature groups.; The Freiheitssatz and its extensions; 1. Introduction; 2. The FHS and Amalgams; 3. The Classical Freiheitssatz and Magnus' Method; 4. Small Cancellation Products and Diagrams; 5. One-Relator Products; 6. One-Relator Products of Cyclics; 7. Multi-Relator Versions of the Freiheitssatz; A Rodrigues-type formula for the q-Racah polynomials and some related results; Air on the Dirac strings; Does Lyndon's length function imply the universal theory of free groups?
- Schottky groups and the boundary of TeichmÃơller space: Genus 2Lacunary series as quadratic differentials in conformal dynamics; The geometry of cycles in the Cayley diagram of a group; Braids, Riemann surfaces and moduli; Some remarks on J replacement in direct products; Wilhelm Magnus, applied mathematician; On the combinatorial curvature of groups of F-type and other one-relator free products; Branched dihedral structures on Riemann surfaces; Groups and Lie algebras: The Magnus theory; Semiregular continued fractions whose partial denominators are 1 or 2.