What is the main conflict in 1Q84 by Haruki Murakami?

Aomame is a fitness trainer and assassin living in Tokyo, Japan, in 1984 who targets abusive men. While enroute to an assassination, she gets stuck in traffic and takes an emergency stairwell off an expressway to save time. She has unwittingly entered a parallel world, which she calls 1Q84 (Q standing for "Question) because she seems to have lost track of time and her understanding of reality has become skewed.