# TTT85: Manchester

MIMS, University of Manchester.

Supported by the London Mathematical Society and MIMS.

## Date

22 October 2012

## Speakers

### Simona Paoli (University of Leicester)

Algebraic models of homotopy types

Algebraic models of homotopy types

Homotopy n-types are CW complexes whose homotopy groups vanish in dimension higher than n. They can be thought of as the building blocks of topological spaces, thanks to a classical construction, the Postnikov decomposition of a space. The problem of finding good algebraic models of homotopy types is a fundamental question in homotopy theory.

In this talk, I will first cover the basic homotopical background concerning n-types. I will then illustrate one such algebraic model, called n-typical n-fold groupoids. The latter is based on a special type of higher groupoidal structure, and has desirable properties. This is joint work with David Blanc.

### Andrew Lobb (University of Durham)

The HOMFLYPT knot invariant and some moduli spaces

The HOMFLYPT knot invariant and some moduli spaces

We discuss the relationship between the colored HOMFLYPT knot invariant and certain moduli spaces which arise in the context of instanton homology. No prior knowledge will be assumed.

### Victor Buchstaber (Steklov Institute and Moscow State University)

Towers of principal S1-bundles and applications

Towers of principal S1-bundles and applications

Towers of smooth principal S1-bundles arise in problems of algebraic topology, differential, symplectic, and contact geometry, the theory of nilpotent Lie groups, and the theory of dynamical systems. In this talk I shall discuss the construction of such towers, and describe several related results and open problems.