Questions: Sema Salur

Nolan Fitzpatrick: Could you explain the title of your 2013 work " Existence of Compatible Contact Structures on G2-manifolds."

Sema Salur:  G_2 manifolds are 7 dimensional spaces which satisfy some important geometric properties. We call them manifolds with special holonomy.

In my paper (joint work with F. Arikan and H. Cho) " Existence of Compatible Contact Structures on G2-manifolds ", we showed that G_2 manifolds carry 

(almost) contact structures. This is interesting because I have this program where I use the (almost) contact structure on 7-manifolds to hunt for the topological description of G_2 holonomy manifolds.

Nolan Fitzpatrick: What is a contact structure?

Sema Salur: A contact structure on a 7 manifold is a 6-plane distribution in the tangent bundle of the G_2 manifold. This distribution is given as 

the kernel of a differential 1-form alpha such that alpha \wedge (d \alpha)^3 is always nonzero. 

Nolan Fitzpatrick: What is an almost contact structure? 

Sema Salur: Almost contact structure is also a 6-dimensional distribution in the tangent 

bundle of G_2 as the kernel of alpha but in this case alpha \wedge (d\alpha)^3 can be zero. Here wedge means exterior product and d \alpha means

the exterior derivative.