This is the 7390th most frequent Russian word.
горбачевой
The word "горбачевой" is the feminine genitive or dative form of the surname "Горбачёв" (Gorbachev), meaning "of Gorbachev" or "to Gorbacheva" depending on context.
In this sentence, "Горбачёвой" is used in the genitive case to specify that the works belong to Galina Gorbacheva, showing possession.
Лекция была на тему творчества Галины Горбачёвой.
The lecture was on the topic of Galina Gorbacheva's works.
Here, "Горбачёвой" indicates locative meaning when referring to a place associated with a person, showing where an action took place.
Мы встретились с автором книги, которую прочли у Горбачёвой.
We met with the author of the book that we read at Gorbacheva's place.
In this context, "Горбачёвой" is in the instrumental case, showing the agent (the doer) of an action in a passive construction.