LS-category of compact Hausdorff foliations
by Hellen Colman and Steven Hurder

HISTORY:

Colman's Thesis defined the leafwise and transverse categories for foliations. This goal of this project was to understand in more depth the properties of the transverse category. Its properties for compact Hausdorff (and more generally compact) foliations turns out to be quite delicate, reflecting properties of the singular leaves as well as usual homotopy considerations. There are many open questions left to pursue.

This project was the result of collaboration between the authors during academic year 1999-2000, while Colman was a Visiting Research Scholar at UIC, funded by a Fellowship for Galician Researchers (from the University of Santiago, Spain.)