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Vronsky does not sleep on the train either. He's happy with the effect that Anna has on him. He feels as if no one else exists for him. He daydreams about Anna and replays all his interactions with her.
The first person he sees when he gets off the train is Anna's husband. He's sort of shocked to see an actual husband.
He goes up to Anna and her husband, bowing to them both and asking Anna if she had a comfortable night.
Anna introduces Vronsky to her husband.
Karenin (Anna's husband) begins talking to Anna, as a cue for Vronsky to leave.
Vronsky asks to call on the Karenins.
Anna and her husband walk away, chatting. Karenin suggests that Anna call on her friend, Countess Lydia Ivanovna, who is a prominent member of Petersburg society.