Constructing equivariant maps for representations

Details Constructing equivariant maps for representations Constructing equivariant maps for representations

2004-05-03

arxiv.org/abs/math/0405028v2

Mathematics

Geometric Topology

Changes from V1: The paper has been substantially reorganised. New applications added. This is the version accepted for pubbli

Scientific paper

We show that if G is a discrete subgroup of the group of the isometries of the hyperbolic k-space H^k, and if R is a representation of G into the group of the isometries of H^n, then any R-equivariant map F from H^k to H^n extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Moreover, under an additional hypothesis, we show that the weak extension we obtain is actually a measurable R-equivariant map from the boundary of H^k to the closure of H^n. We use this fact to obtain measurable versions of Cannon-Thurston-type results for equivariant Peano curves.

Affiliated with

Also associated with

No associations

Rating

Constructing equivariant maps for representations 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 Constructing equivariant maps for representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constructing equivariant maps for representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-235095