Intersection forms (Ex)
From Manifold Atlas
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Determine the [[Intersection form|intersection forms]] of the following $2k$-manifolds: | Determine the [[Intersection form|intersection forms]] of the following $2k$-manifolds: | ||
− | + | # $F_g$ an oriented surface of genus $g$ | |
− | + | # $S^2 \times S^2$ | |
− | + | # $S^2 \tilde \times S^2$, the total space of the non-trivial linear $S^2$-bundle over $S^2$ | |
− | + | # $\CP^2$ | |
− | + | # $M_1 \times M_2$, where $M_i$ are manifolds of dim $k$ and $4-k$, $k \leq 3$ | |
− | + | # $S^4 \times S^4$ | |
− | + | # $\Hh P^2$ | |
− | + | # $\CP^4$ | |
− | + | # $\Oo P^2$ | |
Determine the [[Wikipedia:Signature_(topology)|signatures]] of the manifolds above. | Determine the [[Wikipedia:Signature_(topology)|signatures]] of the manifolds above. | ||
</wikitex> | </wikitex> | ||
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[[Category:Exercises]] | [[Category:Exercises]] | ||
+ | [[Category:Exercises without solution]] |
Latest revision as of 05:30, 3 January 2019
Determine the intersection forms of the following -manifolds:
- an oriented surface of genus
- , the total space of the non-trivial linear -bundle over
- , where are manifolds of dim and ,
Determine the signatures of the manifolds above.