I am currently reading Milnor's paper which discusses the group action on spheres without fixed point. At the second page of the paper, he denotes $$M^n*M^n$$ to be a symmetric product of a manifold. I was confused of what this means, as it does not adjust to any of the definition of the terms on Wikipedia. Any comments in appreciated.

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    $\begingroup$ It should mean $M*M = M\times M/ \sim$, where $(x, y) \sim (y, x)$. $\endgroup$ – user99914 Nov 10 '15 at 12:12
  • $\begingroup$ Is it perhaps the join? $\endgroup$ – Bruno Stonek Nov 10 '15 at 13:00
  • $\begingroup$ I think John's answer should be the original intention. The rest parts says we can 'trivialise' $f_1$, which hence the join does not make sense. $\endgroup$ – Wunderbar Nov 10 '15 at 20:39

It should mean $M*M = M\times M/ \sim$, where $(x, y) \sim (y, x)$. -- John Ma

To confirm that the answer by John Ma is correct, I looked up another paper which gives this definition of symmetric product just before citing the aforementioned Milnor's paper about it.


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