# Mixed vs cyclic homology

### Uli Krähmer (University of Glasgow)

Wednesday 9th November, 2016 16:00-17:00 Maths 522

#### Abstract

Homology is about a sequence of maps $b : C_n \rightarrow C_{n-1}$ with $bb=0$. Cohomology is about maps $d$ that go the other way round. In this talk we'll contemplate what we can do if we have both such a $b$ and such a $d$, and how we can combine the two to define a "mixed" homology. Examples of the main theorem cover cyclic homology of associative algebras and the Hodge theorem for compact smooth manifolds.