As an application of conservation of angular momentum around a fixed axis the following example was given in our textbook. If a girl sitting on a swivel chair starts rotating with her arms streched as shown then her angular speed reduces. Similarly as she brings her arms closer angular velocity automatically increases.
My book explains the following reason, Due to constant angular momentum we have that $Iw$ is constant. As we stretch the arms, the radius increases and as a consequence $w$ decreases and vice versa.
Why at all is the angular momentum conserved in this case? In other words why is net torque zero?