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This question regards a part of the proof of the so called surgery step, in Wall's book "surgery on compact manifolds", Theorem 1.1. Setting $M^m$ smooth manifold, $X$ CW complex, $\phi :M\...

Background: I spent sometime reading about algebraic K-theory and started reading research papers on the subject with relative facility at least I do understand constructions, statements of the ...

A classical result of simply connected surgery theory, is that if two normal maps $f:M_i\rightarrow X$, $i=0,1$ are normally cobordant and if the dimension of the manifolds is odd, there exists a ...

Say we have a periodicity generator $e \in H^k(BG)$. I can show that we then have a $(k-1)$-dimensional $G$-complex $X$ with free $G$-action. It's also not that difficult to see that it has trivial $G$...

There is a theorem by Sullivan of the following form: Theorem: There is an equivalence of $H$-spaces $$ G/PL[\tfrac{1}{2}] \simeq BO_{\otimes}[ \tfrac{1}{2} ]\ . $$ It can be found for example ...