Topological Invariants via Differential Geometry

The use of differential geometry to understand topological properties precedes the formal establishment of Algebraic Topology as a mathematical discipline and has been a central theme in mathematics since the early 20th Century.

The goals of this project fall in this tradition, in that we propose to study a variety of geometric objects and their topological properties using tools from Differential Geometry and Analysis. The main areas of study are the following:

  • Foliations of singular spaces. The main objective is to generalize the theory for regular spaces by using tools of non-commutative geometry.
  • Holonomy and Lie algebroids. A central question is the extension of the notion of parallel transport to higher dimensions, beyond the case of curves.
  • Topology and geometry of moduli spaces. Among the central objects of study are character varieties for surface groups. Through the holonomy representation and non-abelian Hodge theory these spaces are viewed as moduli spaces of gauge theoretic objects, known as Higgs bundles.



Start date: 

Monday, 22 March, 2010

Area / Group: 



Peter Gothen
André Gama Oliveira

Other members: 

João Nuno Gonçalves Faria Martins
Björn Gohla
Ronald Alberto Zuniga Rojas
Azizeh Nozad

Financial support: 

100 000EUR

Funding entity: 


Project reference: