3-DIMENSIONAL NON-COMPACT INFRA-NILMANIFOLDS

  • 발행 : 1999.01.01

초록

Let G be the 3-dimensional Heisenberg group. A discrete subgroup of Isom(G), acting freely on G with non-compact quotient, must be isomorphic to either 1, Z, Z2 or the fundamental group of the Klein bottle. We classify all discrete representations of such groups into Isom(G) up to affine conjugacy. This yields an affine calssification of 3-dimensional non-compact infra-nilmanifolds.

키워드

참고문헌

  1. Annals of Math. v.71 Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups L. Auslander
  2. Annals of Math. v.83 Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups Ⅱ L. Auslander
  3. Bieberbach Groups and Flat Manifolds Leonard S. Charlap
  4. Quarterly J. Math. (Oxford) v.46 Affine structures for closed 3-dimensional manifolds with nil-geometry K. Dekimpe;P. Igodt;S. Kim;K. B. Lee
  5. Quarterly J. Math. (Oxford)(2) v.46 Infra-solvmanifolds of type (R) K. B. Lee
  6. Bull. London Math. Soc. v.15 The geometries of 3-manifolds P. Scott
  7. Spaces of constant curvature J. Wolf