# The Mathematical Heritage of Henri Poincaré

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*Felix E. Browder*

On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This volume presents the written versions of all but three of the invited talks presented at this Symposium (those by W. Browder, A. Jaffe, and J. Mather were not written up for publication). In addition, it contains two papers by invited speakers who were not able to attend, S. S. Chern and L. Nirenberg.

If one traces the influence of Poincari through the major mathematical figures of the early and midtwentieth century, it is through American mathematicians as well as French that this influence flows, through G. D. Birkhoff, Solomon Lefschetz, and Marston Morse. This continuing tradition represents one of the major strands of American as well as world mathematics, and it is as a testimony to this tradition as an opening to the future creativity of mathematics that this volume is dedicated.

This part contains sections on geometry, topology, Riemann surfaces,
discontinuous groups and Lie groups, and several complex variables.

# Table of Contents

## The Mathematical Heritage of Henri Poincare

- Table of Contents v6 free
- Introduction vii8 free
- Summary Chronology of the Life of Henri Poincaré ix10 free
- Section 1. Geometry 114 free
- Web geometry 316
- Problems on abelian functions at the time of Poincaré and some at present 1124
- Hyperbolic geometry: the first 150 years 2538
- Completeness of the Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions 4154
- Symplectic geometry 6174

- Section 2. Topology 7588
- Section 3. Riemann surfaces, discontinuous groups and Lie groups 113126
- Section 4. Several complex variables 187200