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Results tagged with pontrjagin-duality
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user 495347
3
votes
1
answer
74
views
Linking form for homology with general coefficients
For integral homology groups there is the notion of linking form (http://www.map.mpim-bonn.mpg.de/Linking_form)
$$
Tor(H_{l}(X,\mathbb{Z}))\times Tor(H_{n-l-1}(X,\mathbb{Z}))\rightarrow \mathbb{Q}/\ma …
- 839
7
votes
1
answer
217
views
Pontryagin dual of a group-cohomology class
Let $A, B, C$ be finite Abelian groups fitting in a short exact sequence
$$
1 \rightarrow A\overset{\iota}{\rightarrow} B\overset{\pi}{\rightarrow} C\rightarrow 1
$$
This determines a class $[\epsilo …
- 839
1
vote
1
answer
118
views
A map in group cohomology from $H^n(G,G^{\vee})$ to $H^{n+1}(G,U(1))$
Let $G$ be a finite abelian group and denote by $G^{\vee}=\mathrm{Hom}(G,U(1))$ its Pontryagin dual. For any positive integer $n$ one can define a homomorphism of abelian groups
$$
f:H^{n}(G,G^{\vee}) …
- 839