4
votes
1answer
169 views

Codimension zero embeddings and diffeomorphism groups

Let $V$ be a smooth manifold obtained by attaching the ``open collar'' $[0,1)\times \partial N$ to a compact smooth manifold $N$ along the boundary. Let $\mathrm{Emb}(N, V)$ be the space of embeddings ...
6
votes
0answers
117 views

Torsion in Whitehead group

Let $\pi$ be a finite group of odd order. What do we know about the torsion subgroup of $Wh(\pi)$? I am especially interested in the $2$-primary part. Is it always trivial?
7
votes
1answer
308 views

The K-theoretic Farrell-Jones conjecture for cat(0) groups

Is the fibered K-theoretic farrell-jones conjecture true for cat(0)-groups?
6
votes
0answers
260 views

homotopy domination that splits a non-split epimorphism and still wants to be a homotopy equivalence

Can a homotopy domination by a space supporting a free action of $G$ be promoted to a homotopy equivalence with such a space? As stated, this is not a serious question (multiply by an $EG$). But with ...
21
votes
1answer
1k views

Morava on Shafarevich

Jack Morava has some interesting ideas stemming from stable homotopy theory and geometric topology on the Shafarevich Conjecture. The Shafarevich Conjecture states: $Gal(\bar Q / Q_{cycl})$ is free. ...
13
votes
3answers
1k views

Can we decompose Diff(MxN)?

If you have two manifolds $M^m$ and $N^n$, how does one / can one decompose the diffeomorphisms $\text{Diff}(M\times N)$ in terms of $\text{Diff}(M)$ and $\text{Diff}(N)$? Is there anything we can say ...