Pure and Applied Mathematics Quarterly
Volume 16 (2020)
Special Issue: In Honor of Prof. Kyoji Saito’s 75th Birthday
Guest Editors: Stanislaw Janeczko, Si Li, Jie Xiao, Stephen S.T. Yau, and Huaiqing Zuo
Meromorphic connections in filtered $A_\infty$ categories
Pages: 515 – 556
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 $A_\infty$ 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.
filtered $A_\infty$ category, CH structure, mermorphic connection, Euler connection, Getzler–Gauss–Manin connection, cyclic homology, primitive form
2010 Mathematics Subject Classification
Primary 53D37, 53D45. Secondary 18G55.
The first-named author was partially supported by JSPS Grant-in-Aid for Scientific Research (A) No 15H02054 (PI. H. Ohta).
The second-named author was partially supported by JSPS Grant-in-Aid for Scientific Research (A) No 15H02054 and for Young Scientists (B) No 17K17817 (PI. A. Kanazawa).
Received 4 April 2019
Accepted 20 December 2019
Published 11 November 2020