E.Geltzler defined Gauss Manin connection on periodic cyclic homology of smooth proper DG algebra.I just began to learn his definition.But it seems that his construction is very different to the Gauss Manin connection on relative De Rham cohomology(which is differential of $E_1$ term of spectral sequence of De Rham complex)in appearance.Of course,I know the periodic cyclic homology is the "right" analogue of De Rham cohomology.
My question is that how to establish the precise argument to see that these two definitions in algebraic geometric setting and DG(or $A\infty$)setting are compatible.For example,Let $A$ be a smooth proper DG algebra corresponding to a smooth projective variety(for example,say,projective space,then $A:=RHom(E,E)$,where $E$ is generator of derived category of coherent sheaves on projective space).Then we will have periodic cyclic complex,say $C(A,A)$.So what is the right analogue for the filtration of $C(A,A)$ of that of DeRham complex.Then one should be able to get the $E_1$ term of spectral sequence of $C(A,A)$.Does this analogue construction give the right analogue of Gauss Manin connection of periodic cyclic homology? Does it coincide with what E.Geltzler constructed?
Thanks
