Wall's finiteness obstruction

In geometric topology, a field within mathematics, the obstruction to a finitely dominated space X being homotopy-equivalent to a finite CW-complex is its Wall finiteness obstruction w(X) which is an element in the reduced zeroth algebraic K-theory K ~ 0 ( Z [ π 1 ( X ) ] ) {\displaystyle {\widetilde {K}}_{0}(\mathbb {Z} [\pi _{1}(X)])} of the integral group ring Z [ π 1 ( X ) ] {\displaystyle \mathbb {Z} [\pi _{1}(X)]} . It is named after the mathematician C. T. C. Wall.

Source: Wikipedia — Wall's finiteness obstruction (CC BY-SA 4.0)