A∞-Structures and Moduli Spaces

This book discusses certain moduli problems related to A∞-structures. These structures can be viewed as a way of recording extra information on cohomology algebras. They are useful in describing derived categories appearing in geometry, and as such, they play an important role in homological mirror symmetry. The author presents some general results on the classification of A∞-structures and also considers two concrete moduli problems. The first is related to the moduli spaces of curves, while the second is related to the classification of solutions of an associative version of the Yang–Baxter equation