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Let $R$ be a graded ring (concentrated in nonnegative dimensions and maybe bounded from above). For every positive natural number $n$, denote by $R\to\tau_{\leq n}R$ the $n$-truncation and by $\tau_{\geq n}R \to R$ the analogous procedure killing all dimensions below n. These two rings may both be viewed as $R$-modules.

My question is the following: Is there a simple procedure computing $Tor_*^R(\tau_{\leq n}R, \tau_{\geq n+1}R)$ (in the category of graded modules)?

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you tag this with "algebraic topology", so there is a topological background? –  Martin Brandenburg Jul 4 '10 at 15:39
    
probably, sometimes i use the tag because i want the perspective of a topologist who might not otherwise see it. It lets the readers know my leanings. –  Sean Tilson Aug 30 '11 at 21:32

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