Nearby cycles and periodicity in cyclic homology (Q2904905)

The paper is an excerpt of author's doctoral thesis under the supervision of C. Consani. The author considers an \((n+1)\)-dimensional variety \(X\) fibered over the complex unit disk. Let \(D(X)\) be the (non-commutative) ring of \(C^{\infty}\)-differential operators on \(X\). One of the main results of the work asserts that the periodicity operator on the cyclic cohomology of the ring \(D(X)\) can be interpreted as an induced monodromy of the fiber bundle \(X\).NEWLINENEWLINEFor the entire collection see [Zbl 1243.14002].