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Hello,

I'm interested in the question, given

Given $M$ and $N$, two connected orientable manifolds of the same dimension, when is $M$#$N$ independent of the choice of orientations for M$ # $N$ diffeomorphic to $M$ and # $N$? For instance, if \overline{N}$, where $\overline{N}$ is $N$ with the orientation reversed? If $N$ has an orientation-reversing automorphism, it that is this a necessary or sufficient condition for $M$#$N$ to be independent of the choice of orientation on diffeomorphic to $N$?

Thanks--M$#$\overline{N}$? If it isn't a necessary condition, what invariants can be used to distinguish $M$ # $N$ from $M$ # $\overline{N}$? (As a baby example, how does one show that $CP^2$ # $CP^2\ncong CP^2 $#$ \overline{CP ^2}$ ?)

Zygund
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When is the connected sum of manifolds orientation-independent?

Hello,

I'm interested in the question, given $M$ and $N$, two orientable manifolds of the same dimension, when is $M$#$N$ independent of the choice of orientations for $M$ and $N$? For instance, if $N$ has an orientation-reversing automorphism, it that necessary or sufficient condition for $M$#$N$ to be independent of the choice of orientation on $N$?

Thanks--

Zygund