Groups of type FPFP via graphical small cancellation

We construct an uncountable family of groups of type $FP$. In contrast to every previous construction of non-finitely presented groups of type $FP$ we do not use Morse theory on cubical complexes; instead we use Gromov's graphical small cancellation theory.Comment: 3 figures. Second version: two paragraphs added emphasizing the difference between our construction and Morse theoretic one

Realising fusion systems

We show that every fusion system on a p-group S is equal to the fusion system associated to a discrete group G with the property that every p-subgroup of G is conjugate to a subgroup of S

Realising fusion systems

We show that every fusion system (saturated or not) on a p-group S is equal to the fusion system associated to a discrete group G containing S as a subgroup and such that every finite subgroup of G is conjugate to a subgroup of S

The Yagita invariant of symplectic groups of large rank

Fix a prime $p$, and let $R$ be any subring of the complex numbers that is either integrally closed or contains a primitive $p$th root of 1. For each $n\geq p-1$ we compute the Yagita invariant at the prime $p$ for the symplectic group $Sp(2n,R)$.Comment: Minor changes compared to first versio

The ?2-cohomology of hyperplane complements

We compute the l^2-Betti numbers of the complement of any finite collection of affine hyperplanes in complex n-space. At most one of the l^2-Betti numbers is non-zero. <br/