The Bing-Borsuk conjecture is stronger than the Poincaré conjecture

Ricci Flow and the Poincaré Conjecture

The Bing-borsuk and the Busemann Conjectures

We present two classical conjectures concerning the characterization of manifolds: the Bing Borsuk Conjecture asserts that every n-dimensional homogeneous ANR is a topological n-manifold, whereas the Busemann Conjecture asserts that every n-dimensional G-space is a topological n-manifold. The key object in both cases are so-called generalized manifolds, i.e. ENR homology manifolds. We look at t...

The 0/1-borsuk Conjecture Is Generically True for Each Fixed Diameter

In 1933 Karol Borsuk asked whether every compact subset of R can be decomposed into d + 1 subsets of strictly smaller diameter. The 0/1Borsuk conjecture asks a similar question using subsets of the vertices of a ddimensional cube. Although counterexamples to both conjectures are known, we show in this article that the 0/1-Borsuk conjecture is true when d is much larger than the diameter of the ...

The Auslander-Reiten Conjecture for Group Rings

This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...

On stronger versions of Brumer’s conjecture

Let k be a totally real number field and L a CM-field such that L/k is finite and abelian. In this paper, we study a stronger version of Brumer’s conjecture that the Stickelberger element times the annihilator of the group of roots of unity in L is in the Fitting ideal of the ideal class group of L, and also study the dual version. We mainly study the Teichmüller character component, and determ...