arXiv research

Regular neighborhoods of singular submanifolds are isotopic to bundle morphisms.

Study of diffeomorphisms groups on lens spaces with Morse-Bott foliations.

It is well-known that any isotopically connected diffeomorphism group $G$ of a manifold determines uniquely a singular foliation $\F_G$. A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that…

Let $F$ be a smooth foliation on a closed Riemannian manifold $M$, and let $Λ$ be a transverse invariant measure of $F$. Suppose that $Λ$ is absolutely continuous with respect to the Lebesgue measure on smooth transversals. Then a topological definition of the $Λ$-Lefschetz number of any leaf preserving diffeomorphism …

The paper studies diffeomorphisms of a specific foliation on a Klein bottle.

The paper explores higher fixed point theorems for foliations with applications to rigidity and integrality.

The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional Lie(G)-valued 1-form gauge fields so as to lift the symmetry to Maps(Sigma,G). P…