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The Farrell-Jones conjecture for a given group is an important conjecture in manifold theory. I will review some of its consequences and will discuss a class of groups for which it is known, for example 3-manifold groups. Finally, I will discuss a proof that free-by-cyclic groups satisfy FJC, answering a question of Lück.
This is joint work with Koji Fujiwara and Derrick Wigglesworth.
57M20 ; 20F65 ; 57M07 ; 18F25