Natalia Osipova and Ivan Vasiliev were the golden couple of the Bolshoi until they defected to this St. Petersburg troupe in 2011 in search of more artistic freedom. They join the Mikhailovsky in its United States debut at Lincoln Center with a caravan of classics and some newer works. This week, Ms. Osipova is "Giselle," a signature role (she performs Tuesday and Thursday; Mr. Vasiliev on Wednesday evening). Future programs include "The Flames of Paris" (Nov. 14 to 16), "Three Centuries of Russian Ballet" (Nov. 18 and 19) and "Don Quixote" (Nov. 20 to 23).