X-Nico

Assembly map

It may be viewed as a parametrized version of the classical theorem which states that equivalence classes of h-cobordisms on $M$ are in 1-to-1 correspondence with elements in the Whitehead group of $\backslash pi\; 1(M)$.

Direct limit of groups

The Whitehead group of a ring (the first K-group) can be defined in terms of $\backslash operatorname\{GL\}(A)$.

H-cobordism

Whitehead groups Wh(π), where $\backslash pi\; \backslash cong\; \backslash pi\; 1(M)\; \backslash cong\; \backslash pi\; 1(W)\; \backslash cong\; \backslash pi\; 1(N).$

Surgery exact sequence

One way to state the Borel conjecture is to say that for such $X$ we have that the Whitehead group $Wh\; (\backslash pi\; 1\; (X))$ is trivial and that

see also