Spin bordism and elliptic homology.
We show that the objects of Bass-Farrell categories which represent 0 in the corresponding Nil groups are precisely those which are stably triangular. This extends to Waldhausen's Nil group of the amalgamated free product with index 2 factors. Applications include a description of Cappell's special UNil group and reformulations of those splitting and fibering theorems which use the Nil groups.
We show some advantages of splitting vector bundles by blowups.
Soit la -algèbre, ou bien réduite ou bien maximale, associée à la variété feuilletée , et la -algèbre élémentaire des opérateurs compacts. Alors, si dim, on montre que est isomorphe à .
We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space of singular foliations of codimension and degree on the complex projective space , when . We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute their projective degrees in several cases.
In this paper we firstly define a tangential Lichnerowicz cohomology on foliated manifolds. Next, we define tangential locally conformal symplectic forms on a foliated manifold and we formulate and prove some results concerning their stability.