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Universität Augsburg
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Universität Augsburg
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Dr. Felix Schmäschke
Humboldt Universität zu Berlin
spricht am
Montag, 24. Juni 2024
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16 Uhr s.t.
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
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By the work of Quinn, the existence question of the open book decomposition is completely solved in all dimensions except $4$. Quinn showed that a closed manifold of dimension not equal to four carries the structure of an open book if and only if its asymmetric signature vanishes.
In the talk I give an overview of the existence question of open books in general and explain in particular the difficulties which arise in dimension $4$. I will present our main result, which states that an open book on the $3$-sphere extends to an open book of the $4$-ball up to stabilisation provided that the asymmetric signature vanishes. For the proof I discuss a stable version of the $4$-dimensional $s$-cobordism theorem and generalize a theorem of Tuarev saying that any simple homotopy equivalence between compact oriented $3$-manifolds with boundary is homotopic to a diffeomorphism. Furthermore, independently I show our result that any finitely presented group arises as the fundamental group of a closed oriented smooth $4$-manifold that carries an open book. It is a joint work with Marc Kegel. |
| Hierzu ergeht herzliche Einladung. |
| Zhen Gao |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).