Sharing memory between compute shader and pixel shader
well, if anyone is stumbling across this and needs to know what solved it for me: We can bind a compute buffer to global shader memory if we just know what exactly we need to do

within the Compute shader the RWstructuredBuffer is declared as (without the "\" infront of float):

uniform RWStructuredBuffer&lt;\float3&gt; buffer : register(u1);


(not certain whether register(u1) is really needed

within the vert/frag shader the buffer is defined as:

uniform StructuredBuffer&lt;\float3&gt; buffer;   


In a c# script before the first kernel dispatch (we only need to assign this buffer once), I assign the buffer via

buffer = new ComputeBuffer(size, sizeof(float)*3,ComputeBufferType.Default);
Shader.SetGlobalBuffer(Shader.PropertyToID("buffer"), buffer);


It took me ages to find this and it works as far as I can tell. The article I finally stumbled over that did something similar. I do not have to read the data back to cpu with buffer.GetData(container) and put it into the material manually. 
If the compute shader changes the buffer data this will be reflected in the vert/frag shader immediately.