Reidemeister torsion (Ex)

Show that the following finite based free $\Qq$$<wikitex>; Show that the following finite based free $\Qq$-chain compex concentrated in dimensions $, \Qq$-chain compex concentrated in dimensions $2$$2$, $1$$1$ and $0$$0$ is contractible and compute its Reidemeister torsion:

$\displaystyle \Qq \xrightarrow{\left( \begin{array}{c} 0 \\ r \end{array} \right)} \Qq \oplus \Qq \xrightarrow{\left( \begin{array}{cc} 1 & 0 \end{array} \right)} \Qq.$ $$\displaystyle \Qq \xrightarrow{\left( \begin{array}{c} 0 \\ r \end{array} \right)} \Qq \oplus \Qq \xrightarrow{\left( \begin{array}{cc} 1 & 0 \end{array} \right)} \Qq.$$

References

$ and $\Qq$-chain compex concentrated in dimensions $2$$2$, $1$$1$ and $0$$0$ is contractible and compute its Reidemeister torsion:

$\displaystyle \Qq \xrightarrow{\left( \begin{array}{c} 0 \\ r \end{array} \right)} \Qq \oplus \Qq \xrightarrow{\left( \begin{array}{cc} 1 & 0 \end{array} \right)} \Qq.$ $$\displaystyle \Qq \xrightarrow{\left( \begin{array}{c} 0 \\ r \end{array} \right)} \Qq \oplus \Qq \xrightarrow{\left( \begin{array}{cc} 1 & 0 \end{array} \right)} \Qq.$$

References

$ is contractible and compute its Reidemeister torsion: $$ \Qq \xrightarrow{\left( \begin{array}{c} 0 \ r \end{array} \right)} \Qq \oplus \Qq \xrightarrow{\left( \begin{array}{cc} 1 & 0 \end{array} \right)} \Qq. $$ == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises with solution]]\Qq-chain compex concentrated in dimensions $2$$2$, $1$$1$ and $0$$0$ is contractible and compute its Reidemeister torsion:

$\displaystyle \Qq \xrightarrow{\left( \begin{array}{c} 0 \\ r \end{array} \right)} \Qq \oplus \Qq \xrightarrow{\left( \begin{array}{cc} 1 & 0 \end{array} \right)} \Qq.$ $$\displaystyle \Qq \xrightarrow{\left( \begin{array}{c} 0 \\ r \end{array} \right)} \Qq \oplus \Qq \xrightarrow{\left( \begin{array}{cc} 1 & 0 \end{array} \right)} \Qq.$$