Towards Homological Mirror Symmetry

Abstract

This is an expository article on the A-side of Kontsevich's Homological Mirror Symmetry conjecture. We give first a self-contained study of $A_{\infty }$-categories and their homological algebra, and later restrict to Fukaya categories, with particular emphasis on the basics of the underlying Floer theory, and the geometric features therein. Finally, we place the theory in the context of mirror symmetry, building towards its main predictions.

arXiv comment139 pages, 15 figures. Corrected a few minor typos, fixed an issue with hyperlinks

References in corpus (6)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• String Theory on Calabi-Yau Manifolds
• Fukaya categories of the torus and Dehn surgery
• Lectures on Holomorphic Curves in Symplectic and Contact Geometry
• On the homology theory of fibre spaces
• Symplectic homology and periodic orbits near symplectic submanifolds