Memoirs of the American Mathematical Society 2012; 131 pp; softcover Volume: 220 ISBN10: 0821872923 ISBN13: 9780821872925 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/220/1035
 In this paper the authors introduce the notion of a geometric associative \(r\)matrix attached to a genus one fibration with a section and irreducible fibres. It allows them to study degenerations of solutions of the classical YangBaxter equation using the approach of Polishchuk. They also calculate certain solutions of the classical, quantum and associative YangBaxter equations obtained from moduli spaces of (semi)stable vector bundles on Weierstraß cubic curves. Table of Contents  Introduction
 YangBaxter equations
 Massey products and AYBEa single curve
 Massey products and AYBEfamilies of curves
 Explicit calculationssmooth curves
 Explicit calculationssingular curves
 Summary
 Bibliography
