Intersection forms (Ex)

Revision as of 14:50, 1 April 2012

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]]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 signatures of the manifolds above.