## what do empty parens symbol mean?

Quick easy question: what is the meaning of the symbol $(\space\space )$. I've seen it now in two papers, one of which is Milgram's Group Representations and the Adams Spectral Sequence, avaiable at here.

On the top of page 170, Milgram writes $\partial(\space\space) \to S^k\vee S^k\to S^k\to v$

I figure if I knew what was meant by mathematical colloquialism "$\partial(\space \space)$", interpereting this part of the paper would be easy enough, I'm just not sure wht it means.

Thanks

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## 1 Answer

In the case at hand, $v$ is defined as $$v = \bar{u}(id \times A \times A): E_{Z_2} \ltimes D^{r-s} \wedge D^{s-r} \to S$$

The sequence in question, which is described as the 'restriction of $v$ to the boundary', is shorthand for $$\partial(E_{Z_2} \ltimes D^{r-s} \wedge D^{s-r}) \stackrel{\pi}{\to} S^k \vee S^k \to S^k \to S^0$$ and the notation $\partial(\ )$ is shorthand for the boundary of the 'obvious thing', the only space that belongs there. The $\pi$ seems to be projection.

I can't comment on the other occurrence, but often in seminars one can write such a notation when trying to save time and/or space on the board, especially if the expression is complicated.

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Thanks, interpretation makes everything work out. I was having trouble figuring out what the "obvious thing" should be, but I in retrospect it actually is the only thing that fits. – Joseph Victor Aug 17 at 2:33