Universität Augsburg

Herr Jannes Bantje
Universität Münster
spricht am
Montag, 5. Juni 2023
um
16 Uhr s.t.
im
Raum 2004 (L1)
über das Thema:
Abstract: 
Given a smooth manifold one can ask whether there is a metric of positive scalar curvature on it. The study of this existence question has produced many obstructions. The natural followup question is uniqueness of positive scalar curvature metrics. One way to phrase it is „What is the homotopy type of the space of psc metrics?". A central tool used in its study is the index difference by Hitchin, which provides a map to $K$theory. This map is known to be nontrivial on homotopy groups if the dimension of the manifold is at least 6. In my talk I will explain the methods used to prove this detection result and present new enhancements, which allow for a simultaneous extension to dimension 5 and incorporation of the fundamental group (yielding an index difference mapping to the $K$theory of group $C^*$algebras). These enhancements use the original Madsen–Weiss theory and its extension by Perlmutter, which has been dubbed "parametrised Morse theory". This is in contrast to methods of Galatius–RandalWilliams employed in earlier results. 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Bernhard Hanke 
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).