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Consider the map $L_0(\mathbb{Z})\to L_0(\mathbb{Z}_2)$ of Wall L-groups induced by the surjection $\mathbb{Z}\to \mathbb{Z}_2$. Here $\mathbb{Z}_2$ is the cyclic group (field) of order 2. We know tha …

[I thought that I had already posted this question, but I couldn't find it in a search, so I apologize if I'm posting twice.] Let $G$ be a finite group. Then the rational oriented bordism ring $\Omeg …

Let $X$ be an oriented compact manifold of dimension $2k$. Suppose that a compact Lie group $G$ acts differentiably on $X$ in an orientation-preserving way. Let $B$ be the ${\mathbb R}$-bilinear form …

I'm trying to find a reference that discusses the homotopy groups of $\mathrm{MSPL}_k$ and $\mathrm{MSTop}_k$, the Thom spectra for $k$-dimensional oriented PL and Top manifolds. I just need the fact …

In Jim Davis's paper "Manifold aspects of the Novikov conjecture" (Surveys on surgery theory, vol 1, pages 195-224) he writes down (Theorem 6.5) a sort-of converse to the Novikov conjecture. He writes …

Let $E^4$ be the two stage Postnikov space appearing in the homotopy type of the classifying space $G/PL$. One of its properties is that it only has two nontrivial homotopy groups $\pi_2(E)=Z/2Z$ and …