We explain the Farrell-Jones Conjecture for the algebraic K-groups and L-groups of group rings of torsion free groups. It relates them to the homology of the classifying space BG. There is also a more advanced version for arbitrary groups, the Full Farrell-Jones Conjecture and we will explain its status. Actually, it is known to be true for a rather large class of groups including hyperbolic groups, CAT(0)-groups, lattices in almost connected Lie groups and fundamental groups of 3-manifolds. The potential of the Farrell-Jones Conjecture is illustrated by reviewing its many applications to questions about manifolds, algebra, and group theory. For instance it implies in dimensions greater or equal to five the Borel Conjecture which predicts that two aspherical closed topological manifolds are homeomorphic if and only if their fundamental groups are isomorphic. At the very end we give a brief survey about the strategy of proofs.

Meeting ID: 916 5855 1117

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Contact: Aru Ray, Tobias Barthel,Viktoriya Ozornova**Slides:** are attached below or see our Nextcloud

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