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Universität Augsburg
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Universität Augsburg
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Dominik Wrazidlo
Universität Heidelberg
spricht am
Montag, 7. November 2016
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| A theorem by Saeki asserts that, in high dimensions, groups of homotopy spheres are canonically isomorphic to cobordism groups of special generic functions. This result indicates that definite fold singularities play a part in the detection of exotic differentiable structures on spheres. Inspired by subsequent questions that arise naturally in the context of Banagl's positive TFT which is based on fold maps into the plane, we subject special generic functions to an equivalence relation coarser than that of cobordism by also allowing for indefinite fold singularities in a controlled way. As our main result reveals, indefinite fold singularities perceive a subtle kind of information about the structure of groups of homotopy spheres. In fact, the detected information is strongly related to a filtration by subgroups featuring homotopy spheres that can be bounded by cobordisms of prescribed connectedness. As an application of our theorem, we show that indefinite fold lines of middle absolute index are capable of detecting the Kervaire sphere in certain dimensions. |
| Hierzu ergeht herzliche Einladung. |
| Kai Cieliebak |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).