Meromorphic connections in filtered $A_{\infty}$ categories

Abstract

In this note, introducing notions of CH module, CH morphism and CH connection, we define a meromorphic connection in the "z-direction" on periodic cyclic homology of an A∞ category as a connection on cohomology of a CH module. Moreover, we study and clarify compatibility of our meromorphic connections under a CH module morphism preserving CH connections at chain level. Our motivation comes from symplectic geometry. The formulation given in this note designs to fit algebraic properties of open-closed maps in symplectic geometry.

Categorical primitive forms of Calabi-Yau $A_\infty$-categories with semi-simple cohomology

“…. m of Jac(PO M ), there is an object in the Fukaya category whose endomorphism algebra A k is a Clifford algebra as defined in (20) with λ k the critical value PO M (p k ) and h We conclude that in this case HH • (Fuk(M )) and the map CO satisfy all the conditions of Theorem 5.9, thus the result follows from the theorem. where the coproduct is taken over distinct critical values λ of W .…”

“…, d n ). We can define a new Clifford algebra, denoted by CL, with generators X i and relations as in (20), with the matrix H replaced by diag(d 1 , . .…”