A _∞-Structures and Moduli Spaces

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Front matter
Introduction
1 Homological background
	1 A_∞- and A_n-structures
	2 Homological perturbation
	3 Relation of A_∞-structures to Hochschild cohomology
	4 Massey products for A_∞-categories and twisted objects
	5 Triangulated structure and generators
	6 Cyclic A_∞-structures
	7 G-invariant A_∞-structures
2 Moduli spaces of A_∞-structures
	8 The moduli problem
	9 Nice quotients
	10 Representability theorem
	11 A_∞-structures with a segment of defining higher products
	12 A class of minimally nonformal algebras
3 A_∞-structures and moduli of curves
	13 Examples of calculations for curves
	14 A_∞-structures and curves with nonspecial divisors
	15 Representability of the moduli of A_∞-structures
	16 Comparison of the moduli spaces via deformation theory
	17 Invariants of curves via A_∞-structures
	18 Case n=g
	19 Case of genus 0
	20 Case of genus 1
	21 Hyperelliptic moduli
4 Pairs of 1-spherical objects, A_∞-structures, and Yang–Baxter equations
	22 A_∞-structures associated with 1-spherical pairs
	23 Solutions of the associative Yang–Baxter equation and 1-spherical pairs
	24 Another approach to the moduli space of A_∞-structures
References
Index
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