  Topological magnon bands and magnon Hall effect in insulating collinear
ferromagnets are induced by the Dzyaloshinskii-Moriya interaction (DMI) even at
zero magnetic field. In the geometrically frustrated star lattice, a
coplanar/noncollinear $\mathbf q=0$ magnetic ordering may be present due to
spin frustration. This magnetic structure, however, does not exhibit
topological magnon effects even with DMI in contrast to collinear ferromagnets.
We show that a magnetic field applied perpendicular to the star plane induces a
non-coplanar spin configuration with nonzero spin scalar chirality, which
provides topological effects without the need of DMI. The non-coplanar spin
texture originates from the topology of the spin configurations and does not
need the presence of DMI or magnetic ordering, which suggests that this
phenomenon may be present in the chiral spin liquid phases of frustrated
magnetic systems. We propose that these anomalous topological magnon effects
can be accessible in Polymeric Iron (III) Acetate --- a star-lattice
antiferromagnet with both spin frustration and long-range magnetic ordering.
