A∞-Structures and Moduli Spaces / Alexander Polishchuk.

Format:

Book

Author/Creator:

Polishchuk, Alexander, author.

Language:

German

Subjects (All):

Categories (Mathematics).

Physical Description:

1 online resource (178 pages)

Place of Publication:

Berlin : EMS Press, 2022.

Summary:

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. For example, he gives a sufficient criterion for the existence of a finite-type moduli scheme of A ∞ ​ -structures extending a given associative algebra. He also considers two concrete moduli problems for A ∞ ​ -structures. 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. The book will be of interest to graduate students and researchers working in homological algebra, algebraic geometry, and related areas.

Contents:

Front Matter

Contents

Introduction

1 Homological background

2 Moduli spaces of A ∞-structures 3 A ∞-structures and moduli of curves

4 Pairs of 1-spherical objects, A ∞-structures, and Yang-Baxter equations

References

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-9854752-6-1