| Commensurability and Virtual Fibration for Graph Manifolds (2007) | |||||||||||||||
Abstract | |||||||||||||||
| y class of compact geometric 3-manifolds with the given structure (two for the last two geometries if orientation-preserving commensurability of oriented manifolds is considered). For the remaining non-hyperbolic geometry Sol, the commensurability classes are in one-one correspondence with real quadratic number fields (such a manifold is covered by a torus bundle over a circle and the field in question is the field generated by an eigenvalue of the monodromy of this bundle). Non-compact finite volume non-hyperbolic geometric 3-manifolds admit geometric structures of both types H 2 \Theta E 3 and PSL and form just one commensurability class, also in the oriented case. In section 2 we define several multiplicative invariants for prime 3-manifolds. A multiplicative invariant is one that multiplies by degree for covering spaces. Our invariants are most interesting fo | |||||||||||||||
Publication details | |||||||||||||||
| |||||||||||||||