On the Connes operator in Hochschild homology

Bitjong Ndombol
Let K be a field of characteristic p ≥ 0 and X a topological space. If N * X is the algebra of normalized singular cochains on X with coefficients in K, then a product is defined on the negative Hochschild complex C * X := C * N * X ([2]) which induces a natural commutative graded algebra structure on HC * X := HH * X. We prove that if X is simply connected, the Connes operator B : C * X → C * +1 X is an algebra derivation in homology.