Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg

 

Oberseminar Differentialgeometrie

 

Dr. Renée Hoekzema
University of Oxford

 
spricht am
 
Montag, 15. Januar 2018
 
um
 
16:00 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Manifolds with odd Euler characteristic and higher orientability«

Abstract:
Orientable manifolds have even Euler characteristic unless the dimension is a multiple of 4. I give a generalisation of this theorem: k-orientable manifolds have even Euler characteristic (and in fact vanishing top Wu class), unless their dimension is 2k+1m for some integer m. Here we call a manifold k-orientable if the ith Stiefel-Whitney class vanishes for all 0< i< 2k. This theorem is strict for k=0,1,2,3, but whether there exist 4-orientable manifolds with an odd Euler characteristic is a new open question. Such manifolds would have dimensions that are a multiple of 32. I discuss manifolds of dimension high powers of 2 and present the results of calculations on the cohomology of the second Rosenfeld plane, a special 64-dimensional manifold with odd Euler characteristic.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Fabian Hebestreit
 

Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).



wwwadm@Math.Uni-Augsburg.DE,    Mo 8-Jan-2018 14:44:15 MEZ