##### Department of Mathematics,

University of California San Diego

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### Math 292A - Topology/Geometry

## Ralph Kaufmann

#### Max-Planck Institute, Bonn

## The link between Cacti, Connes-Kreimer's Hopf algebraand Deligne's Conjecture

##### Abstract:

We will introduce several varieties of cacti operadswhich are interrelated by direct and semi-direct products.These operads can all be naturally realized as suboperadsof the arc operad. Furthermore the homotopy equivalence ofof these operads to the little discs and framed little discspoints the way to Deligne's conjecture. In this direction, wewill also consider operations on Hochschild cohomology.On the other hand, but astonishingly in the same spirit,we will show how the non-trivial coproduct of the renormalizationHopf algebra of Connes and Kreimer can also be undersood as beingnatural when viewed in terms of our arc operad composition.

Host: P. Teichner

### February 14, 2003

### 3:00 PM

### AP&M 7218

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