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Vronsky's outer life has not changed one bit since his affair with Anna.
He still hangs out with his military friends, (a.k.a. his regiment). They all love him, and he loves them back.
He doesn't mention his love to any of them, but the entire Petersburg society knows that an affair is taking place between Vronsky and Anna. Karenin's important standing puts a massive spotlight on their affair.
Everyone gets ready for the relationship to go public—all the women who don't like Anna are preparing the nasty things they'll send through the gossip mill.
Vronsky's mother approved of the affair at first, when she thought that Vronsky was having an elegant affair with a prominent society woman.
Vronsky's mother is not so pleased, however, when she realizes that it's a passionate, desperate affair that results in Vronsky turning down promotions in order to remain near Anna.
Vronsky's second passion is for horses, which gives him some time away from his primary passion (i.e., Anna).
His regiment has planned a race for the officers. It's a steeplechase (an obstacle course for horses over three miles of open ground) for which Vronsky had registered and bought a special English thoroughbred mare. In spite of his distracting love for Anna, Vronsky is pretty excited about this event.