Research Area F*: ‘Structures and invariants in algebra and topology’
The Research Area F* started in 10/2012.
This is a new research area formed by researchers, half of whom came to Bonn after the cluster started. The research area also reﬂects a new emphasis in topology and representation theory.
The activities of this research area aim at the interplay of geometry, topology, algebra and group theory. The topics range over
- the classiﬁcation of manifolds,
- algebraic K- and L-theory of group rings,
- the geometry and homology of mapping class groups,
- equivariant and global homotopy theory,
- and categoriﬁcation of knot invariants and group algebras.
They have in common that they lead to explicit invariants in geometry and topology, designed to answer speciﬁc questions and solve speciﬁc problems, and to a better and deeper understanding of important general structures, which are of basic fundamental interest and will open the door to new projects and proofs. The investigators are experts in different ﬁelds; their respective backgrounds and expertise will lead to a fruitful cooperation and an exchange of knowledge and techniques.