When they arrive in Petersburg, Vronsky and Anna live in separate suites of rooms.
Vronsky is fooling himself as to what Anna's reception will be in polite society.
Russian society can be harsh. If a woman does something that's not allowed—say, leaving her husband for another man—she will be shut out of society.
Because of Anna's behavior, her former friends ignore her, no one invites her to parties, and if people she used to know see her in public, they pretend she isn't there. Anna's friends risk being ostracized themselves if they try to reach out to her. Vronsky hopes that the people closest to Anna will ignore this social pressure, but he's wrong.
After finding out that there was no official divorce, Princess Betsy's enthusiasm for hanging out with Anna is gone. She does visit Anna, but only for ten minutes, and only to make a point of her loyalty.
Vronsky hopes his sister-in-law, Varya, will not refuse to see Anna, but Varya gently says no. She makes it clear that her decision is merely a reflection of what society demands.
As a result, Vronsky and Anna spend their time in Petersburg as if it's a foreign city—except that Karenin's name seems to come up everywhere.
Throughout their stay, Anna has been in a strange mood. Vronsky is confused and feels that Anna is hiding something from him.