Intersection forms (Ex)

Latest revision as of 05:30, 3 January 2019

Determine the intersection forms of the following $<wikitex>; Determine the [[Intersection form|intersection forms]] of the following k$-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 -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. </wikitex> [[Category:Exercises]] [[Category:Exercises without solution]]2k$-manifolds:

1. $F_g$ an oriented surface of genus $g$
2. $S^2 \times S^2$
3. $S^2 \tilde \times S^2$, the total space of the non-trivial linear $S^2$-bundle over $S^2$
4. $\CP^2$
5. $M_1 \times M_2$, where $M_i$ are manifolds of dim $k$ and $4-k$, $k \leq 3$
6. $S^4 \times S^4$
7. $\Hh P^2$
8. $\CP^4$
9. $\Oo P^2$

Determine the signatures of the manifolds above.