  The influence of confinement on the topological phases of superfluid 3He is
studied using the torsional pendulum method. We focus on the phase transition
between the chiral A-phase and the time-reversal-invariant B-phase, motivated
by the prediction of a spatiallymodulated (stripe) phase at the A-B phase
boundary. We confine superfluid 3He to a single 1.08 {\mu}m thick nanofluidic
cavity incorporated into a high-precision torsion pendulum, and map the phase
diagram between 0.1 and 5.6 bar. We observe only small supercooling of the
A-phase, in comparison to bulk or when confined in aerogel. This has a
non-monotonic pressure dependence, suggesting that a new intrinsic B-phase
nucleation mechanism operates under confinement, mediated by the putative
stripe phase. Both the phase diagram and the relative superfluid fraction of
the A and B phases, show that strong coupling is present at all pressures, with
implications for the stability of the stripe phase.
