A note on commuting foliations (2012)

 

03/June/2012

I just modified the text a bit and submitted it on arxiv

PDF File.

08/May/2012

A preliminary working version is available here: PDF File.

10 pages. Wrote down the results in the regular case. Will probably add a section about singularities to make this note more substantial.

07/May/2012

8 pages (9 pages by mid-day). Snail speed, 1 page/day. Nothing very exciting, but someone has to do it and fix the notion of commuting foliations :-)

Will try to finish this small note within 2-3 days, by the deadline. The problem of singularities of commuting foliations will require lots of work. In this note I write mainly about normal forms in the regular case.

05/May/2012

Only 6 pages so far. Lot of other things to do, so can’t write this one very fast. But hopefully will finish it in a week or so.

The main idea is to study the properties and normal forms of commuting Nambu structures and their associated foliations. I wrote down simple local normal from theorems in the regular case. I still have to work on the (simultaneous) normal forms for commuting Nambu structures near a singular point, and also on the semi-local and global picture (in the regular case first).

Start date: 02/May/2012

Expected finish date: 10/May/2012

This is a small paper that I’m writing on the generalization of the notions of commutativity and integrability from the category of vector fields to the category of singular foliations. Apparently, these notions have not been defined for general foliations before. They are rather natural, and lead to interesting geometric objects.

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