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Universität Augsburg
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Universität Augsburg
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Dr. Nathan Perlmutter
Stanford University
spricht am
Montag, 24. Juli 2017
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| In this talk I will construct a cobordism category consisting of manifolds equipped with a choice of Morse function, whose critical points occupy a prescribed range of degrees. My main result identifies the homotopy type of the classifying space of this cobordism category with that of the infinite loopspace of a certain Thom spectrum. This result can be viewed as an analogue of the celebrated theorem of Galatius, Madsen, Tillmann and Weiss. In the second part of the talk I will show how to use the cobordism category to probe the homotopy type of the space of positive scalar curvature metrics on a closed, spin manifold of dimension ≥ 5. This construction uses a parametrized version of the Gromov-Lawson construction developed by Walsh and Chernysh. Our main result detects many non-trivial homotopy groups in the space of positive scalar curvature metrics and gives an alternative proof and slight extension of a recent breakthrough theorem of Botvinnik, Ebert, and Randal- Williams. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Bernhard Hanke |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).