Usually it is explained, that paired-end sequencing is useful for determining with more certainty where the reads come from (which can be useful if we have many repeat regions).
For paired-end reads, TopHat2 processes the two reads separately through the same mapping stages described above. In the final stage, the independently aligned reads are analyzed together to produce paired alignments, taking into consideration additional factors including fragment length and orientation.
1) If the reads are aligned separately, doesn't that contradict the basic idea of paired-end sequencing (to get a more precise mapping) ??
2) Perhaps what I lack to know the answer is an understanding of the final stage. It'd be great if someone could refer me to an explanation. I didn't find one in the forums.