Foliation-preserving Maps Between Solvmanifolds

Details Foliation-preserving Maps Between Solvmanifolds Foliation-preserving Maps Between Solvmanifolds

1998-02-10

arxiv.org/abs/math/9802133v1

Mathematics

Geometric Topology

Scientific paper

For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliation F_i of the homogeneous space Gamma_i\G_i. Let f be a continuous map from Gamma_1\G_1 to Gamma_2\G_2 whose restriction to each leaf of F_1 is a covering map onto a leaf of F_2. If we assume that F_1 has a dense leaf, and make certain technical technical assumptions on the lattices Gamma_1 and Gamma_2, then we show that f must be a composition of maps of two basic types: a homeomorphism of Gamma_1\M_1 that takes each leaf of F_1 to itself, and a map that results from twisting an affine map by a homomorphism into a compact group. We also prove a similar result for many cases where G_1 and G_2 are neither solvable nor semisimple.

Affiliated with

Also associated with

No associations

Rating

Foliation-preserving Maps Between Solvmanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Foliation-preserving Maps Between Solvmanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Foliation-preserving Maps Between Solvmanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-489445