Greg Graviton
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 Jan14 awarded Good Answer Dec9 awarded Caucus Nov14 comment Striking applications of integration by parts @JakobH Note that the integration variable $t$ has a minus sign, $f(x-t)$. Oct1 revised Action of $G/H$ on $H_n(H;M)$ Add concrete calculation with diagrams Sep30 awarded Explainer Aug17 awarded Good Answer Aug6 accepted Action of $G/H$ on $H_n(H;M)$ Aug6 comment Action of $G/H$ on $H_n(H;M)$ Many thanks for your answer! (I'll make a small edit and add the concrete calculation later.) Brown's book was not available in my university's library. A book by Lang mentioned that the action on the zeroth homology uniquely determines the action on higher homology groups via the long exact sequence / uniqueness of group homology, but a concrete calculation using this method seemed very daunting to me. Aug6 awarded Custodian Aug6 reviewed Approve Evaluate the limit as $x$ approaches $3$ : $\displaystyle\frac{x^3 -6x+2}{x^2+2x-3}$ Aug3 comment Action of $G/H$ on $H_n(H;M)$ @tj_ Apparently, I'm missing the definition of the action. Could you elaborate it into a short answer? That would be much appreciated. Aug3 comment Action of $G/H$ on $H_n(H;M)$ @tj_ Both are possible, the definition of homology is symmetric with respect to which module you resolve. Aug2 comment Action of $G/H$ on $H_n(H;M)$ Oh! But wouldn't this mean that the Hochschild-Serre spectral sequence has only limited utility? Right now, it seems to me that in order to calculate the G/H action, I have to look at the bar resolution of $M$ as a $\mathbb{Z}[G]$-module, which I wanted to avoid doing in the first place by decomposing $G$ into $H$ and $G/H$. (Of course, I need some information about how $H$ sits inside $G$.) I was hoping for some "functorial" way of defining the action on $H_n(H;M)$. Aug1 revised Action of $G/H$ on $H_n(H;M)$ Fixed resolution Aug1 asked Action of $G/H$ on $H_n(H;M)$ Jul29 awarded Yearling Jul2 awarded Curious Jul1 awarded Notable Question Dec19 awarded Nice Answer Jul29 awarded Yearling