You would use the preposition k in Russian with verbs of 'going'
to indicate going to a person's place. The person to whose place you
are going, or whom you are going to see will be in the dative case:
Я иду к Антону.
I am going to Anton's.
Они идут к учительнице.
They are going to the teacher's place (to see the teacher).
The preposition по will always require a noun in the dative case.