Frame Bundle Freeness Results

Thursday, April 24, 2014 - 10:30am - 11:30am
Lind 305
Scot Adams (University of Minnesota, Twin Cities)
In smooth dynamics of Lie groups, it's a consequence of the Frobenius Theorem that locally free actions have a foliated orbit structure. This allows for the formation of local transversals which reduces the classification of the orbits down to a problem in countable equivalence relations. For actions that are not locally free, this fails, but it's natural to ask if one can work around this difficulty by finding a related action that is locally free, and, with luck, even free. Passage to higher order frame bundles (and various associated bundles) is one technique for implementing this work-around. We will discuss situations where freeness can be found in frame bundles, and situations where it cannot.