While answering this question my interest in the rotation/reflection group was piqued.
I personally know very basic group theory, not much more than what a group really is. I understand that the techniques I used in the answer to that question are similar to group theoretical techniques.
Could someone explain how chirality appears in $n$ dimensional objects living in $m>n$ dimensional space if and only if $n=m$ using group theory? Preferably (but not necessarily) giving some background on the techniques being used to better suit my current understanding of group theory.
Note thatwhen I say an $n$ dimensional object, I mean an object that can occupy a minimum of $n$ dimensions. A helix is thus a "three dimensional object", even if its topological dimension is 1.
Apologies if the question is too broad.