  Engineering non trivial topological phases in materials, specially
skyrmion-like arrangements, has been of great interest in the last decade due
to its potential technological applications. In this work, we study a model of
electrons coupled to a magnetic texture in the kagome lattice interacting with
magnetic moments via Rashba spin orbit coupling in the large Hund interaction
limit. We obtain the effective spin Hamiltonian and study the emergent low
temperature phases under an external magnetic field using large scale Monte
Carlo simulations. We show that strong geometric frustration, characteristic of
the kagome lattice, and the competition between the effective exchange,
antisymmetric and anisotropic couplings, gives rise to a large variety of
non-trivial topological phases. On the one hand, for antiferromagnetic exchange
coupling a pseudo-antiferromagnetic skyrmion crystal is stabilized for a broad
range of parameters. As the exchange coupling gets smaller, chiral single-q and
double-q phases emerge. On the other hand, in the ferromagnetic case, even
though the competition of the different interactions produce a series of exotic
textures, a remarkable parallel may be drawn with the pure ferromagnetic model
with antisymmetric interactions. Finally, for the special case where the
exchange coupling is completely suppressed, we show that, coming from a higher
temperature cooperative paramagnet, an "umbrella-like" plaquette order with
semiextensive degeneracy is induced by the external magnetic field.
