Suspension of a symmetric complex (Ex)

Using the definition and the $\omega$$<wikitex>; Using the definition and the $\omega$ from Exercise [[Structured chain complexes III (Ex)]] show that $$ S(\varphi)_0 = 0 $$ and for $s \geq 0$ $$ S(\varphi_{s+1}) = \pm \varphi_s $$ </wikitex> == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]]\omega$ from Exercise Structured chain complexes III (Ex) show that

$\displaystyle S(\varphi)_0 = 0$ $$\displaystyle S(\varphi)_0 = 0$$

and for $s \geq 0$$s \geq 0$

$\displaystyle S(\varphi_{s+1}) = \pm \varphi_s$ $$\displaystyle S(\varphi_{s+1}) = \pm \varphi_s$$