PREFACE

The First International Meeting on Geometry and Topology was held at Universidade do Minho, in Braga, on the 11th, 12th and 13th of September 1997, as the first conference of a series we hope will continue to gather geometers and topologists working on different subjects in Mathematics.

There were essentially two reasons that led to the organization of this scientific meeting:

• Geometry and Topology are two domains in fundamental research which naturally interact and establish a support for many different areas in Mathematics and Mathematical Applications. Some new results recently found brought new subjects and new approaches to both Geometry and Topology, broadening their fields of research and showing the importance of their study and knowledge. The growing role that the study of Geometry now plays in all processes of Mathematical Education reflects what has just been pointed out.

• In Portugal, there are some research groups in some specific areas of Geometry and Topology that foster meetings in their very specific subjects to promote and discuss their research. However, the remaining geometers and topologists who have different interests, work in very small local groups or just alone. There is little communication between Portuguese mathematicians working in similar areas and the only contact with geometers, topologists or schools in other countries that exists is often with the school where the Portuguese mathematician completed his post-graduate education.

Therefore, the main aim of the organizers of the First International Meeting on Geometry and Topology was to promote future working contacts between geometers and topologists, both Portuguese or from other countries, by creating an opportunity for the exchange and discussion of ideas between the participants. We like to believe that this aim was fulfilled.

We must acknowledge and thank the invaluable support we received from the Scientific Committee both during the preparation of the conference and during the event itself. Professors Luis A. Cordero, Francisco Craveiro de Carvalho, James Eells, Armando Machado, Luísa Magalhães and Stewart A. Robertson helped us with their experience, dealing with various scientific matters including the acceptance of communications. We could always rely on their support.

We would like to thank Professors Werner Ballmann, Robert Osserman, Dietmar Salamon and Alberto Verjovsky who promptly accepted our invitation.

We also want to thank the presence and participation of all the mathematicians who took part in the conference and their contribution to the good atmosphere one could feel during the event.

Last but not the least, we must thank Ms Alexandra Pereira, who helped us so much before, during and after the meeting, dealing with paperwork and always willing to help.

To both of us, the First International Meeting on Geometry and Topology has been a good and valuable experience that we plan to continue in a near future. We just hope the same is true for most of the participants.

Braga and Porto, October 1998.

Ana Pereira do Vale

Rosário Pinto

We gratefully acknowledge the support of

Junta Nacional de Investigação Científica Centro de Matemática da Universidade do Minho Universidade do Minho Fundação Luso-Americana para o Desenvolvimento Caixa Geral dos Depósitos Atlantis – Crisal Cristais de Alcobaça Vieira de Castro – Produtos Alimentares S. A. Livraria Minho Câmara Municipal de Braga Biblioteca Pública de Braga Arquivo Distrital de Braga Região de Turismo Verde-Minho Mosteiro de S. Martinho de Tibães

Ana Pereira do Vale and Rosário Pinto