This course covers some applications of algebraic K-theory (in
particular the class group K_0) in geometric/algebraic topology.
We will primarily cover the Wall finiteness obstruction which is a
K-theoretic invariant designed to detect whether certain topological
spaces are homotopy equivalent to finite CW-complexes.
After discussing the fundamentals of the finiteness obstruction, we will
develop some K-theoretic machinery to give a proof of West's theorem.
As an application of West's theorem, we will see that every compact
topological manifold has the homotopy type of a finite CW-complex.
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