**Contemporary Mathematics**

Volume: 169;
1994;
499 pp;
Softcover

MSC: Primary 20; 30; 33;

Print ISBN: 978-0-8218-5156-2

Product Code: CONM/169

List Price: $102.00

AMS Member Price: $81.60

MAA Member Price: $91.80

**Electronic ISBN: 978-0-8218-7760-9
Product Code: CONM/169.E**

List Price: $102.00

AMS Member Price: $81.60

MAA Member Price: $91.80

# The Mathematical Legacy of Wilhelm Magnus: Groups, Geometry and Special Functions

Share this page *Edited by *
*William Abikoff; Joan S. Birman; Kathryn Kuiken*

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 focus of the book is on active areas of current research where Magnus' influence can be seen. The papers range from expository articles to major new research, bringing together seemingly diverse topics and providing entry points to a variety of areas of mathematics.

#### Readership

Research mathematicians.

# Table of Contents

## The Mathematical Legacy of Wilhelm Magnus: Groups, Geometry and Special Functions

- Contents vii8 free
- Preface ix10 free
- Inequalities for plane quasiconformal mappings 112 free
- A look at the Bateman project 2940
- Linear-central filtrations on groups 4556
- Musings on Magnus 99110
- The monodromy group of a transcendental function 107118
- Finite-dimensional representations of Artin's braid group 123134
- Squaring rectangles: The finite Riemann mapping theorem 133144
- 0. Introduction. 134145
- 1. Squared rectangles. 135146
- 2. Optimal weight functions. 144155
- 2.1. The classical Riemann mapping theorem. 145156
- 2.2. The finite problem and the existence and uniqueness of its solution. 146157
- 2.3. The geometry of an optimal weight function: general results. 147158
- 2.4. The geometry of an optimal weight function: special results for quadrilaterals and rings. 151162

- 3. The finite Riemann mapping theorem. 160171
- 4. Algorithms which calculate the finite Riemann mapping. 164175
- 4.1. The minimal path algorithm. 164175
- 4.2. Proofs of the claims about the minimal path algorithm. 166177
- 4.3. The efficiency of the minimal path algorithm. 174185
- 4.4. Flow diagrams and a hybrid algorithm for the finite Riemann mapping problem. 174185
- 4.5. An example of the effectiveness of the hybrid algorithm. 175186

- 5. Optimal weight functions for 2-layer valence 3 tilings of quadrilaterals. 176187
- 6. Approximating combinatorial moduli. 195206
- 7. Variable negative curvature versus constant curvature groups. 209220

- The Freiheitssatz and its extensions 213224
- A Rodrigues-type formula for the q-Racah polynomials and some related results 253264
- Air on the Dirac strings 261272
- Does Lyndon's length function imply the universal theory of free groups? 277288
- Schottky groups and the boundary of Teichmüller space: Genus 2 283294
- Lacunary series as quadratic differentials in conformal dynamics 307318
- The geometry of cycles in the Cayley diagram of a group 331342
- Braids, Riemann surfaces and moduli 341352
- Some remarks on J replacement in direct products 353364
- Wilhelm Magnus, applied mathematician 365376
- On the combinatorial curvature of groups of F-type and other one-relator free products 373384
- Branched dihedral structures on Riemann surfaces 385396
- Groups and Lie algebras: The Magnus theory 397408
- Semiregular continued fractions whose partial denominators are 1 or 2 407418
- Testing for the center of a one-relator group 411422
- Generalizing the Baer-Stallings pregroup 415426
- On binary σ-invariant words in a group 431442
- Explicit matrices for Fuchsian groups 451462
- Levi-properties generated by varieties 467478
- Chains of primitive ideals 475486
- Families of closed geodesics on hyperbolic surfaces with common self-intersections 481492
- On the isometry groups of hyperbolic manifolds 491502
- A generalization of Lazard's theorem on modular dimension subgroups 497508