# Topology

## The Topology of Azumaya Algebras

## Disconnecting the G_2 Moduli Space

Little is currently known about the global properties of the moduli space of a closed 7-manifold, ie the space of Riemannian metrics with holonomy modulo diffeomorphisms. A holonomy metric has an associated -structure, and I will define a Z/48 valued homotopy invariant of a -structure in terms of the signature and Euler characteristic of a Spin(7)-coboundary. I will describe examples of manifolds with holonomy metrics where the invariant is amenable to computation in terms of eta invariants, and which are candidates for having a disconnected moduli space. This is joint work in progress with Diarmuid Crowley and Sebastian Goette.

## Universal torsion, L^2-invariants, polytopes and the Thurston norm

We introduce universal torsion which is defined for -acyclic manifolds with torsion free fundamental group and takes values in certain -groups of a skew field associated to the integral group ring. It encompasses well-know invariants such as the Alexander polynomial and -torsion. We discuss also twisted -torsion and higher order Alexander polynomials which can also be derived from the universal invariant and assign certain polytopes to the universal torsion. This gives especially in dimension 3 interesting invariants which recover for instance the Thurston norm.

## Introduction to the Farrell-Jones Conjecture

## Decision problems, curvature and topology

## Khovanov homology

Lecture notes on Khovanov homology.

## Duality Notes

These are notes for the Duality talk presented as part of the West Coast Algebraic Toplogy Summer School.

## Verlinde Algebra

Lecture Notes on Verlinde Algebra

## WCATSS Problem Set 5

This is the third problem of the West Coast Algebraic Topology Summer School (WCATSS)

## WCATSS Problem Set 4

This is the third problem of the West Coast Algebraic Topology Summer School (WCATSS)