Measurable versions of the LS category on laminations

Details Measurable versions of the LS category on laminations Measurable versions of the LS category on laminations

2011-08-30

arxiv.org/abs/1108.5927v2

Mathematics

Dynamical Systems

22 pages

Scientific paper

We give two new versions of the LS category for the set-up of measurable laminations defined by Berm\'udez. Both of these versions must be considered as "tangential categories". The first one, simply called (LS) category, is the direct analogue for measurable laminations of the tangential category of (topological) laminations introduced by Colman Vale and Mac\'ias Virg\'os. For the measurable lamination that underlies any lamination, our measurable tangential category is a lower bound of the tangential category. The second version, called the measured category, depends on the choice of a transverse invariant measure. We show that both of these "tangential categories" satisfy appropriate versions of some well known properties of the classical category: the homotopy invariance, a dimensional upper bound, a cohomological lower bound (cup length), and an upper bound given by the critical points of a smooth function.

Affiliated with

Also associated with

No associations

Rating

Measurable versions of the LS category on laminations 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 Measurable versions of the LS category on laminations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Measurable versions of the LS category on laminations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-729010