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Whitehead torsion

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In geometric topology, a field within mathematics, the obstruction to a homotopy equivalence f : X → Y {\displaystyle f\colon X\to Y} of finite CW-complexes being a simple homotopy equivalence is its Whitehead torsion τ ( f ) {\displaystyle \tau (f)} which is an element in the Whitehead group Wh ⁡ ( π 1 ( Y ) ) {\displaystyle \operatorname {Wh} (\pi _{1}(Y))} . These concepts are named after the mathematician J. H. C. Whitehead.