Poincare posed his famous question at the end of a long article,
  published in 1904, devoted to studying the topology of 3-dimensional
  manifolds.. Many consider that this paper marks the founding of
  Topology as an independent area of Mathematics. It is certainly true
  that in this paper Poincare introduces many of the ideas that lie at
  the heart of the study of topology of 3-manifolds and indeed of
  manifolds of all dimensions. In this talk we will review what
  Poincare did in his seminal paper and how the topological ideas he
  introduced morphed and evolved over the next 100 years in the hands
  of successive generations of topologists...