Description
This project is concerned with the problem of classifying different smooth structures admitted by a smooth manifold up to homotopy. This classification is made possible by the tools of surgery theory and is summarized in the notion of the smooth structure set $\mathcal{S}^{DIFF}(X)$ of a smooth manifold $X$. We focus on cases when $X$ is the product of the complex projective space with a $k$-dimensional disk. As a result, we obtain a full classification in dimensions $n,k\leq6$. By comparing these results to known computations of the topological structure set $\mathcal{S}^{TOP}(\mathbb{C}P^n\times D^k)$ we obtain examples of "exotic" topological manifolds, that is manifolds with no admissible smooth structure.
| Pracovisko fakulty (katedra)/ Department of Faculty | Katedra algebry a geometrie |
|---|---|
| Tlač postru/ Print poster | Nebudem požadovať tlač posteru / I don't require to print the poster |
