Jonathan Block and Shmuel Weinberger

Higher Todd Classes and Holomorphic Group Actions

This paper attempts to provide an analogue of the Novikov conjecture for algebraic (or Kähler) manifolds. Inter alia, we prove a conjecture of Rosenberg’s on the birational invariance of higher Todd genera. We argue that in the algebraic geometric setting the Novikov philosophy naturally includes non-birational mappings.

Examples of exotic stratifications

We produce examples of manifold stratified pairs in which the lower strata do not have neighborhoods that are mapping cylinders of fiber bundles, or even block bundles. Moreover, the examples do not improve in this regard under stabilization by products with tori. The examples are locally conelike and the lower strata do have neighborhoods which are mapping cylinders of manifold approximate fib...

On the generalized Nielsen realization problem

The main goal of this paper is to give the first examples of equivariant aspherical Poincaré complexes, that are not realized by group actions on closed aspherical manifolds M . These will also provide new counterexamples to the Nielsen realization problem about lifting homotopy actions of finite groups to honest group actions. Our examples show that one cannot guarantee that a given action of ...

Arithmetic Manifolds of Positive Scalar Curvature

Variations on a Theme of Borel