EVENT DETAILS AND ABSTRACT

Title: Periodic cyclic complex as a homotopy crystal
Speaker: Boris Tsygan
Speaker Info: Northwestern University
Brief Description:
Special Note: First talk of Noncommutative geometry seminar
Abstract:

The periodic cyclic complex of an associative algebra is a noncommutative generalization of the complex computing the singular cohomology of a finite dimensional algebraic variety over the complex numbers. The key property of the periodic cyclic complex in characteristic zero is its rigidity under deformations given by a theorem of Goodwillie. It turns out that a similar rigidity property holds for algebras over the integers. Namely, for two multiplications on the sale A that differ by a multiple of a prime p>2, the periodic cyclic complexes of corresponding algebras are isomorphic canonically up to all higher homotopies.