Topological Invariants via Differential Geometry
Research project funded by FCT (Portugal);
information on the FCT page can be found here.
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.
Information for members
- Suggested phrase for including in papers:
Partially supported by FCT (Portugal) with European Regional Development Fund (COMPETE) and national funds
through the project PTDC/MAT/098770/2008.
Last modified: October 11, 2012