Aditi Kar

Rank gradient and cost of Artin groups and their relatives

We prove that the rank gradient vanishes for mapping class groups of genus bigger than 1,

Asymptotically CAT(0) groups

Aut(F_n)

On Property (FA) for wreath products

, for all

On growth of homology torsion in amenable groups

n

Ping Pong on CAT(0) cube complexes

,

A topological splitting theorem for Poincaré duality groups and high-dimensional manifolds

Out(F_n)

Some non-amenable groups

for

Relative ends, L^2 invariants and Property (T)

n \geq 3

Uniform exponential growth for CAT(0) square complexes

, and any Artin group whose underlying graph is connected. These groups have fixed price 1. We compute the rank gradient and verify that it is equal to the first

On Deficiency Gradient of Groups

L^2