Narrow-band HST imaging has resolved the detailed internal structure of the 10 kpc diameter H α+[N II] emission line nebulosity in NGC4696, the central galaxy in the nearby Centaurus cluster, showing that the dusty, molecular, filaments have a width of about 60 pc. Optical morphology and velocity measurements indicate that the filaments are dragged out by the bubbling action of the radio source as part of the active galactic nucleus feedback cycle. Using the drag force we find that the magnetic field in the filaments is in approximate pressure equipartition with the hot gas. The filamentary nature of the cold gas continues inwards, swirling around and within the Bondi accretion radius of the central black hole, revealing the magnetic nature of the gas flows in massive elliptical galaxies. HST imaging resolves the magnetic, dusty, molecular filaments at the centre of the Centaurus cluster to a swirl around and within the Bondi radius