Poincaré duality III (Ex)
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For $S^1$, why is the correct involution for Poincaré Duality $$ \Sigma {a_jt^j}\mapsto \Sigma a_j \omega (t) t^{-j} $$ and not $$ \Sigma{a_jt^j}\mapsto \Sigma a_j \omega (t) t^j ~? $$ | For $S^1$, why is the correct involution for Poincaré Duality $$ \Sigma {a_jt^j}\mapsto \Sigma a_j \omega (t) t^{-j} $$ and not $$ \Sigma{a_jt^j}\mapsto \Sigma a_j \omega (t) t^j ~? $$ | ||
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Latest revision as of 14:56, 1 April 2012
Let be
- the Klein bottle
Consider all possible representations . Compute
For , why is the correct involution for Poincaré Duality
and not