2
$\begingroup$

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.

$\endgroup$
  • 4
    $\begingroup$ 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
1
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.