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Feb, 2020
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Topology and Computer

There are two major relations betweeen topology and computer:

  • applications of topology to computer science, and
  • the use of computer for computations in topology.

The former is new and many interesting ideas have been discovered. For example, Gaucher introduced the notion of model category in the study of parallel processing. It seems that Voevodsky began to apply homotopy theory to logic and computer science.

There are, of course, attempts for computing homology and homotopy groups by using computer. One of the most popular projects is the computation of the stable homotopy groups of spheres by using the Adams spectral sequence .

Nowadays, it is not hard to manipulate topological objects such as simplicial complexes and surfaces on computer displays. Probably visualizations by computer will be useful when teaching undergraduate students.