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Details of talk

TitleA functorial approach to classifying manifolds
PresenterCsaba Nagy (The University of Melbourne)
Author(s)Mr Csaba Nagy
SessionCategory Theory, Algebraic Topology, K-Theory
Time16:30:00 2017-12-12

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.