The Long Line

  title={The Long Line},
  author={Richard Koch},
In dimension greater than or equal to four, it has been proved that a complete classification is impossible (although there are many interesting theorems about such manifolds). The idea of the proof is interesting: for each finite presentation of a group by generators and relations, one can construct a compact connected 4-manifold with that group as fundamental group. Logicians have proved that the word problem for finitely presented groups cannot be solved. That is, if I describe a group G by… CONTINUE READING