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Surojit Ghosh
Surojit Ghosh
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Question:Let G$G$ be a finite abelian group and X$X$ be a G-set. K$K$ be a subgroup of G$G$. let i$i$ be a group homomorphism from K$K$ to G $G$ . I am looking for the map i* = res : H^{a}{G}(X,M) --> H^{i*a}{K}(iX,iM).$$ i^{*} : H^{\alpha}_{G}(X,M) \rightarrow H^{i^{*}\alpha}_{K}(i^*X,i^*M).$$How can I compute this map $i^{*}$ for a constant Mackey functor $M$? Where aWhere $\alpha$ belongs to RO(G)$RO(G)$ and iX = X with K action induced by G. Note: For constant G- Mackecy fuctor M, iM$i^{*}X = X$ with $K$ - action induced by $G$. Note: For constant $G$- Mackecy fuctor $M$, $i^{*}M$ is M$M$ as constant Mackey functor of K$K$. Can Can anyone give some hint atleast for X= point$X= point$.

Question:Let G be a finite group and X be a G-set. K be a subgroup of G. let i be a group homomorphism from K to G . I am looking for the map i* = res : H^{a}{G}(X,M) --> H^{i*a}{K}(iX,iM).How can I compute this map for a constant Mackey functor ? Where a belongs to RO(G) and iX = X with K action induced by G. Note: For constant G- Mackecy fuctor M, iM is M as constant Mackey functor of K. Can anyone give some hint atleast for X= point.

Question:Let $G$ be a finite abelian group and $X$ be a G-set. $K$ be a subgroup of $G$. let $i$ be a group homomorphism from $K$ to $G$ . I am looking for the map $$ i^{*} : H^{\alpha}_{G}(X,M) \rightarrow H^{i^{*}\alpha}_{K}(i^*X,i^*M).$$How can I compute this map $i^{*}$ for a constant Mackey functor $M$? Where $\alpha$ belongs to $RO(G)$ and $i^{*}X = X$ with $K$ - action induced by $G$. Note: For constant $G$- Mackecy fuctor $M$, $i^{*}M$ is $M$ as constant Mackey functor of $K$. Can anyone give some hint atleast for $X= point$.

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Surojit Ghosh
Surojit Ghosh
  • 745
  • 3
  • 8

Calculation of Restriction Map

Question:Let G be a finite group and X be a G-set. K be a subgroup of G. let i be a group homomorphism from K to G . I am looking for the map i* = res : H^{a}{G}(X,M) --> H^{i*a}{K}(iX,iM).How can I compute this map for a constant Mackey functor ? Where a belongs to RO(G) and iX = X with K action induced by G. Note: For constant G- Mackecy fuctor M, iM is M as constant Mackey functor of K. Can anyone give some hint atleast for X= point.