Especially in speaking, we sometimes use so in front position in short responses with reporting verbs such as believe, say, tell, hear, read:
She’s the most popular singer. So everybody says, anyway.
Janet got the job.
SoI heard. (I heard that Janet got the job.)
The Council has given planning permission for another shopping centre in the city.
SoI read in the paper. (I read that the Council has given planning permission for another shopping centre.)
So am I, so do I, Neither do I
We use so with be and with modal and auxiliary verbs to mean ‘in the same way’, ‘as well’ or ‘too’. We use it in order to avoid repeating a verb, especially in short responses with pronoun subjects. When we use so in this way, we invert the verb and subject, and we do not repeat the main verb (so + verb [= v] + subject [= s]):
Geoff is a very good long-distance runner and so[V]is[S]his wife.
What are you doing tonight?
I’ve got loads of exam marking to do and I’m staying at home.
They all joined the new gym and after three weeks so[V]did[S]he. (… and after three weeks he joined the gym too.)
Neither do I
We also use not…either, nor or neither when we want to give a negative meaning: