  We present a detailed investigation of the topological phases and Majorana
fermion (MF) excitations that arise from the bulk interplay between
(un)conventional one/two-band spin-singlet superconductivity and a number of
magnetic texture crystals. The latter define inhomogeneous magnetization
profiles which consist of a periodically-repeating primitive cell. Here we
focus on magnetic texture crystals with a primitive cell of the helix, whirl,
and skyrmion types, which feature distinct symmetry properties. We identify a
multitude of accessible topological phases which harbor flat, uni- or
bi-directional, (quasi-)helical, or chiral MF edge modes. This rich variety
originates from the interplay between topological phases with gapped and nodal
bulk energy spectra. The types of the emerging topological superconducting
phases and the features of the arising MFs are solely determined by the
properties and compatibility of the so-called magnetic and pairing point/space
groups. Our analysis is general and does not rely on specific parameters of the
models employed here to exemplify the topological scenarios which become
accessible. Therefore, our results can be extended to systems with multiple
bands, are relevant for a wide range of layered materials and hybrid devices,
and provide predictions for strong, weak and crystalline topological phases.
