Timeline for Concrete formula for Shapiro's Lemma
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2020 at 1:17 | answer | added | Harshit Yadav | timeline score: 1 | |
| May 8, 2018 at 14:15 | comment | added | Rene Recktenwald | @tj_: Could you explain what the inverse is? | |
| Jan 9, 2017 at 11:36 | comment | added | Mark Wildon | A related question: mathoverflow.net/a/256208/7709. | |
| Jan 9, 2017 at 5:21 | review | Close votes | |||
| Jan 9, 2017 at 11:04 | |||||
| Jan 9, 2017 at 2:17 | comment | added | tj_ | It's more interesting to define the inverse and to show that they compose on cocycle level to the identity up to a coboundary. | |
| Jan 9, 2017 at 2:15 | comment | added | tj_ | Let $\pi: \text{Coind}^G_H(M) = Hom_H(\mathbb{Z}G,M)\to M,\, x \mapsto x(1)$. The isomorphism $\varphi: H^\ast(G,\text{Coind}^G_H(M)) \to H^\ast(H,M)$ from Shapiro's lemma can be described in the following way: Let $f: G \times \cdots \times G \to Hom_H(\mathbb{Z}G,M)$ be a cocycle. Then $\varphi([f])$ is represented by the cocycle $\pi \circ f: H \times \cdots \times H \to M$ (see Brown, Cohomology of Groups, III.8, exercise 2). | |
| Jan 9, 2017 at 0:47 | review | First posts | |||
| Jan 9, 2017 at 1:09 | |||||
| Jan 9, 2017 at 0:44 | history | asked | Shawn Cui | CC BY-SA 3.0 |