Computational Topology

The authors of this article believe there is or should be a research area appropriately referred to as computational topology. Its agenda includes the identification and formalization of topological questions in computer applications and the study of algorithms for topological problems. It is hoped this article can contribute to the creation of a computational branch of topology with a unifying influence on computing and computer applications. Keywords. Survey; topology, geometry, algorithms, computer applications. INTRODUCTION The title of this article combines computation with topology, suggesting a general research activity that studies the computational aspects of problems with topological flavor. What we have in mind is distinctly different from studying the topology of computing or the computer animation of topology. Computational studies of topological questions can be found in the mathematics and the computer science literature, but no concerted effort is apparent. The auth..