I am looking for references with examples about computing induced orientation given a self homeomorphism of a closed orientable n-topological manifold.
I have in mind only A.Hatchers Algebraic Topology who defines induced orientation as follows:
Let $M^n$ a closed orientable n-topological manifolds and $f:M^n\rightarrow M^n$ a homeomorphism. Consider the induced map $f_*:H_n(M;\mathbb{Z})\rightarrow H_n(M;\mathbb{Z})$ and define the fundamental class $[M]$ of $M$ as an element of $H_n(M;\mathbb{Z})$ whose image in $H_n(M,M\setminus\{x\};\mathbb{Z})$ is a generator (using the fact that $H_n(M,M\setminus\{x\};\mathbb{Z})\cong \mathbb{Z}$). Then $f$ is orientation preserving (orientation reversing) if $f_*([M])=[M]$ ($f_*([M])=-[M]$).