# Volume 17 (2013) No. 2

## Volume 17 (2013) No. 2

### Configuration space integrals and the topology of knot and link spaces

Ismar Volić

**Abstract:**

This article surveys the use of configuration space integrals in the study of the topology of knot and link spaces. The main focus is the exposition of how these integrals produce finite type invariants of classical knots and links. More generally, we also explain the construction of a chain map, given by configuration space integrals, between a certain diagram complex and the deRham complex of the space of knots in dimension four or more. A generalization to spaces of links, homotopy links, and braids is also treated, as are connections to Milnor invariants, manifold calculus of functors, and the rational formality of the little balls operads.

### Topological chiral homology and configuration spaces of spheres

Oscar Randall-Williams

**Abstract:**

We compute the rational homology of all spaces of finite configurations on spheres. Our tool is a bar spectral sequence which can be viewed as coming from the notion of “topological chiral homology”, though we give a self-contained construction of the spectral sequence.

### Cooperads as symmetric sequences

Benjamin Walter

**Abstract:**

We give a brief overview of the basics of cooperad theory using a new definition which lends itself to easy example creation and verification and avoids common pitfalls and complications caused by nonassociativity of the composition operation for cooperads. We also apply our definition to build the parenthesization and cosimplicial structures exhibited by cooperads and give examples.

### Moduli spaces and modular operads

Jeffrey Giansiracusa

**Abstract:**

We describe a generalised ribbon graph decomposition for a broad class of moduli spaces of geometric structures on surfaces (with nonempty boundary), including moduli of spin surfaces, $r$-spin surfaces, surfaces with a principle $G$-bundle, surfaces with maps to a background space, surfaces with Higgs bundle, etc.