- 9/12/2017: The extended v -invariant — progress and problems
- 6/07/2017: Disconnecting the G2 moduli space
- 9/6/2016: Connected components of the moduli space of G2 manifolds
TITLE: The extended v -invariant — progress and problems
ABSTRACT: We recall the definition of the extended -invariant, which distinguishes connected components of the moduli space of compact Riemannian manifolds whose holonomy group is (-manifolds for short). All known computations of for -manifolds give values that are divisible by three. This implies that all these examples are topologically -nullbordant. It is therefore interesting to know if for all -manifolds. We will report on results and projects related to this question.
June 7, 2017
TITLE: Disconnecting the G2 moduli space
September 6, 2016
TITLE: Connected components of the moduli space of G2 manifolds
ABSTRACT: The Crowley-Nordström -invariant distinguishes topological structures on 7-manifolds. It takes values in /48. There is a -valued extension for manifolds of holonomy . We will introduce both invariants and show how they can be computed for extra twisted connected sums using -invariants of Dirac operators. This allows us to exhibit examples of 7-manifolds where the space of -holonomy metrics is disconnected.
We will then talk about some related open questions and problems and sketch possible next steps in our research program.