Kaledin Classes and Formality Criteria

Speaker: Dr. Coline Emprin，Stockholm University

Title: Kaledin Classes and Formality Criteria

Language: English  

Time & Venue: 2026.06.03   15:00-17:00   MCM110 Online (Zoom ID: 3329836068  Password: mcm1234)

Abstract: A differential graded algebra A is said to be formal if it is connected to its homology H(A) by a zigzag of quasi-isomorphisms preserving the underlying type of algebraic structure. Formality can be studied using cohomological operations called Massey products. If a differential graded algebraic structure is formal, then all its Massey products vanish. However, the converse is false. Kaledin classes were introduced as a refinement of these Massey products, providing a complete characterization of formality for associative algebras over a field of characteristic zero. In this talk, I will present a generalization of Kaledin classes to arbitrary coefficient rings, as well as to other algebraic structures (encoded by operads). I will also prove new formality criteria based on these classes and discuss some examples.