I am currently reading the book "A short introduction to Topological insulators" by Asboth etal.
In the first chapter on SSH model, they argue (see sec 1.5.3) that number of edge states is a topological invariant for SSH. I have some specific issues in the argument that follows:-
The first line reads: "Consider energy eigenstates at left end of a ..." - What exactly is meant by left end here? Do they mean states localised on the left end?
This seems a bit ambiguous since their plot in fig.1.4 highlights two edge states, which are hyrbidization of left and right localised states. So in that case, what would "energy eigenstates at left end" correspond to?
"Number of 0 energy states is finite because of gap in the bulk" - Why? (this is to be true even when $N \rightarrow \infty$ as stated in beginning of their argument)
At the end, why is $N_A-N_B$ called the "net" number of edge states on sublattice A at left end? From what I understand till now, $N_A$ states have support on sublattice A while $N_B$ states have it on sublattice B. So why call their difference as "net" states on sublattice A?
Thanks in advance for the help ;)