Hilbert ’ s 3 rd Problem and Invariants of 3 { manifolds

  title={Hilbert ’ s 3 rd Problem and Invariants of 3 \{ manifolds},
  author={Walter D. Neumann},
This paper is an expansion of my lecture for David Epstein’s birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3{ manifolds. This \logical progression" makes a good story but distorts history a bit: the ultimate aims of the characters in the story were often far from 3{manifold theory. We start in section 1 with an exposition of the current state of Hilbert’s 3rd problem on scissors congruence for… CONTINUE READING
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