Whitehead torsion II (Ex)

Let $f \colon X \to Y$$<wikitex>; Let $f \colon X \to Y$ be a homotopy equivalence of finite CW complexes. Show that $f \times \text{id}_{S^1} \colon X \times S^1 \to Y \times S^1$ is a [[Wikipedia:simple homotopy equivalence|simple homotopy equivalence.]] This is {{citeD|Kreck&Lück2005|Ex 6.2}}. </wikitex> [[Category:Exercises]] [[Category:Exercises with solution]]f \colon X \to Y$ be a homotopy equivalence of finite CW complexes. Show that $f \times \text{id}_{S^1} \colon X \times S^1 \to Y \times S^1$$f \times \text{id}_{S^1} \colon X \times S^1 \to Y \times S^1$ is a simple homotopy equivalence.

This is [Kreck&Lück2005, Ex 6.2].