# Details of talk

Title | A functorial approach to classifying manifolds |
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Presenter | Csaba Nagy (The University of Melbourne) |

Author(s) | Mr Csaba Nagy |

Session | Category Theory, Algebraic Topology, K-Theory |

Time | 16:30:00 2017-12-12 |

Abstract | The aim of this talk is to show how basic concepts of category theory can be used in the classification of smooth manifolds. We consider smooth simply-connected $n$-manifolds $M$ with $([n/2]-1)$-skeleton a given CW-complex $K$ and $H_{[n/2]}(M)=0$. These manifolds form a finitely generated abelian group $\Theta_n(K)$, and it can be shown that $\Theta_n$ is a functor from the category of CW-complexes to groups. Computation of $\Theta_n(K)$ relies on (among other things) a generalization of Haefliger's exact sequence involving groups of links, which also turns out to be natural in $K$. As an example I will present the computation of $\Theta_8(K)$ in the case when $K$ is a wedge of 2-spheres. If time permits I will also talk about the role of $\Theta_n(K)$ in the classification of a larger class of manifolds. |