Unfortunately, due to my ignorance, my present knowledge is limited to the cobordism Theory of Differentiable Manifolds.

- Cobordism Theory for DIFF/Differentiable/smooth manifolds

However, there are Topological Manifolds which are not Differentiable Manifolds.

So my question here for experts is that what do I need to beware and pay attention in order to master a cobordism theory of Topological Manifolds? What are the

main differences of the computations of the bordism groups for the given following structures:Say,

Cobordism Theory of TOP/topological manifolds

Cobordism Theory for PDIFF/piecewise differentiable manifolds

Cobordism Theory for PL/piecewise-linear manifolds

p.s. Are there Spin, Pin$^+$, and Pin$^-$ versions of these cobordism theories of Topological Manifolds computed in the literature explicitly?