2026/01/31 by Zihong Chen
#math.QA #math.AT #math.SG
We study equivariant operations on the periodic cyclic homology of dg algebras that arise from the chain level action of the two-colored Kontsevich-Soibelman operad. The first main result is that these operations are covariantly constant with respect to the Getzler-Gauss-Manin connection on the periodic cyclic homology of a family of dg algebras. Then, using classical computations of Cohen \citeCoh, we explicitly compute a set of generators for these operations under composition, and show that these generators are closely related to the p-fold equivariant cap products previously studied by the author \citeChe2 in relation to equivariant Gromov-Witten theory with mod p coefficients. The main technical novelty is a re-formulation of the Kontsevich-Soibelman operad in terms of a two-colored version of the cacti operad, and a proof that it is equivariantly quasi-equivalent to the two-colored operad of little disks on a disk/cylinder.