TOPOLOGY SEMINAR

**"****Algebraic Topology of
and Coassociative-Free Immersions into G_2 Holonomy Riemannian 7-Manifolds****"**

By

**Abstract: ****In
this talk, we give a survey of various results about the topology of oriented
Grassmannian bundles related to the exceptional Lie group G_2. Some of these
results are new. One often encounters these spaces when
studying submanifolds of manifolds with calibrated
geometries. As an application we deduce existence of certain special 3 and 4
dimensional submanifolds of G_2 holonomy Riemannian manifolds with
special properties. These are called Harvey-Lawson(HL) pairs. Which
appeared first in the work of Akbulut & Salur about G_2
dualities. Another application is to the coassociative-free embeddings. We
show that if there is a coassociative-free embedding of a
4-manifold into the Euclidean 7-space then the signature vanishes along
with the Euler characteristic. The converse of this theorem is
proved in the more general sense by İ.Ünal using
h-principle techniques. We will talk about this direction if
time permits. Joint work with S.Akbulut and İ.Ünal.**

**Date: ****Monday, December 7, 2015**

**Time: ****13.40 – 14:30**

**Place: ****Mathematics Seminar Room,
SA-141**

**All are most cordially invited.
Tea and cookies will be served after the talk.**