what do empty parens symbol mean? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T19:43:31Z http://mathoverflow.net/feeds/question/104877 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/104877/what-do-empty-parens-symbol-mean what do empty parens symbol mean? Joseph Victor 2012-08-16T23:23:32Z 2012-08-17T06:07:27Z <p>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 <a href="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.pjm/1102968426" rel="nofollow">here</a>. </p> <p>On the top of page 170, Milgram writes $\partial(\space\space) \to S^k\vee S^k\to S^k\to v$</p> <p>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. </p> <p>Thanks</p> http://mathoverflow.net/questions/104877/what-do-empty-parens-symbol-mean/104887#104887 Answer by David Roberts for what do empty parens symbol mean? David Roberts 2012-08-17T02:23:54Z 2012-08-17T06:07:27Z <p>In the case at hand, $v$ is defined as $$v = \bar{u}(id \times A \times A): E_{Z_2} \ltimes D^{r-s} \wedge D^{s-r} \to S$$</p> <p>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.</p> <p>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.</p>