**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

1997; 255 pp; Hardcover

MSC: Primary 57; 58; Secondary 00

Print ISBN: 978-0-8218-0807-8

Product Code: TRANS2/180

Print ISBN: 978-0-8218-0807-8

Product Code: TRANS2/180

List Price: $114.00

Individual Member Price: $91.20

**Electronic ISBN: 978-1-4704-3391-8
Product Code: TRANS2/180.E**

List Price: $114.00

Individual Member Price: $91.20

# Topics in Singularity Theory: V. I. Arnold’s 60th Anniversary Collection

Share this page *Edited by *
*A. Khovanskiĭ; A. Varchenko; V. Vassiliev*

“We were fortunate. We studied under Arnold. We moved in his orbit and had the opportunity to discuss with him everything under the sun. For every one of us this was a rare gift, a great good fortune in our lives.”

—from the Introduction

Leading mathematician and expert teacher, V. I. Arnold turned 60 in June of
1997. This volume contains a selection of original papers prepared for the
occasion of this 60th anniversary by former students and other participants in
Arnold's Moscow seminar. A weekly event since the mid-1960s, this seminar and
its participants have been inspired by Arnold's creative ideas and universal
approach to mathematics.

The papers in this volume reflect Arnold's wide range of interests and his
scientific contributions, including singularity theory, symplectic and contact
geometry, mathematical physics, and dynamical systems. The spirit of this work
is consistent with Arnold's view of mathematics, connecting different areas of
mathematics and theoretical physics. The book is rich in applications and
geometrical in nature.

#### Readership

Graduate students, research mathematicians and theoretical physicists interested in singularity theory, symplectic and contact geometry, topological field theory and dynamical systems.

# Table of Contents

## Topics in Singularity Theory: V. I. Arnold's 60th Anniversary Collection

- Cover Cover11
- Frontispiece iv5
- Title page v6
- Copyright page vi7
- Contents vii8
- Preface ix10
- On the geometry of caustics 116
- Lagrangian embeddings and Lagrangian cobordism 1328
- Polynomial invariants of Legendrian links and plane fronts 2540
- Solutions of the elliptic qKZB equations and Bethe ansatz I 4560
- Singular deformations of Lie algebras. Example: Deformations of the Lie algebra 𝐿₁ 7792
- On imaginary plane curves and spin quotients of complex surfaces by complex conjugation 93108
- Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture 103118
- On a problem of B. Teissier 117132
- Embedding theorems for local maps, slow-fast systems and bifurcation from Morse-Smale to Smale-Williams 127142
- Topological invariants of fiber singularities 141156
- Informal complexification and Poisson structures on moduli spaces 147162
- Consistent partitions of polytopes and polynomial measures 157172
- On primitive elements in the bialgebra of chord diagrams 167182
- Spaces of meromorphic functions on Riemann surfaces 175190
- Hamiltonian loops and Arnold’s principle 181196
- Singularities in the presence of symmetries 189204
- Discrete versions of the four-vertex theorem 197212
- Excitation of elliptic normal modes of invariant tori in Hamiltonian systems 209224
- Ramified coverings of 𝑆² with one degenerate branching point and enumeration of edge-ordered graphs 219234
- On zeros of the Schwarzian derivative 229244
- Stratified Picard-Lefschetz theory with twisted coefficients 241256
- Back Cover Back Cover1273