Poincaré duality (Ex)
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* $H_*(\RP^n; \Zz)$ | * $H_*(\RP^n; \Zz)$ | ||
* $H_*(\RP^n; \Zz_\omega)$ | * $H_*(\RP^n; \Zz_\omega)$ | ||
− | * $H_*(S^{n-1} \tilde times S^1; \Zz)$ | + | * $H_*(S^{n-1} \tilde \times S^1; \Zz)$ |
− | * $H_*(S^{n-1} \tilde times S^1; \Zz_\omega)$ | + | * $H_*(S^{n-1} \tilde \times S^1; \Zz_\omega)$ |
* $H_*(\RP^n \sharp N; \Zz_\omega)$ | * $H_*(\RP^n \sharp N; \Zz_\omega)$ | ||
− | * $H_*(*S^{n-1} \tilde times S^1) \sharp N; \Zz_\omega)$ | + | * $H_*(*S^{n-1} \tilde \times S^1) \sharp N; \Zz_\omega)$ |
</wikitex> | </wikitex> | ||
== References == | == References == | ||
{{#RefList:}} | {{#RefList:}} | ||
[[Category:Exercises]] | [[Category:Exercises]] |
Revision as of 17:01, 9 February 2012
Let denote homology with local co-efficients in twisted the orientation character of a compact manifold , let denote the total space of the non-trivial linear sphere bundle over and let be a closed simply connected manifold.
Determine the following homology groups (in terms of where appropriate