81 research outputs found
Category and compact leaves
No full textAbstractWe prove that if F is a C1–foliation of a compact manifold M with finite transverse saturated LS category, cats(M,F)<∞, then F has a compact leaf. In contrast, we show that if F is expansive on some non-trivial minimal set of F, then cats(M,F)=∞. Examples of foliations are given to illustrate the main results of the paper
A product theorem for ΩBΓG
No full textAbstractThis paper gives a product decomposition theorem for the space ΩBΓG of loops on the classifying space of G-foliations. The proof is based on some observations about the interrelation of G with FГG, the homotopy fiber of the natural map v:BГG→BG. Some applications and consequences of the main theorem are given. We make a conjecture, which is confirmed in low codimensions by our results, about the loop space ΩBГq for the classifying space BГq of smooth codimension-q foliations
Rigid secondary characteristic classes
No full textWe construct families of non-trivial universal rigid secondary classes for
foliations, and then discuss their application to prove that foliations are not
homotopic. An observation of Lawson about the non-triviality of the normal
Pontrjagin classes of foliations is extended, and then used to construct new
families of examples of foliations with non-trivial rigid secondary classes.
Examples are given of (abstractly constructed) foliations of compact manifolds
with homotopic tangent bundles, but which are not homotopic as foliations
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