IPM Calendar 
Sunday 18 March 2018   Today  
Events for day: Saturday 13 January 2018    
           13:00 - 15:00     Geometry and Topology Seminar
Riemannian $7$- and $8$-manifolds with holonomy groups $G2$ and $Spin(7)$


Holonomy group of an oriented Riemannian manifold $M$, is an important invariant of the metric. For a generic metric this group is $SO(n)$, but for some special $g$, the holonomy group can be a proper lie subgroup of $SO(n)$. The possibilities for holonomy group are classified by Berger's theorem.
There are two exceptional holonomy groups, $Spin(7)$ and $G2$. The holonomy group $G2$ happens in dimension $7$ and $Spin(7)$ in dimension $8$. There are constructions due to Joyce which proves the existence of compact manifolds with exceptional holonomy groups, motivated by Kummer constructions. ...