Image of J in the classical Adams Spectral Sequence - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T18:11:44Z http://mathoverflow.net/feeds/question/106268 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/106268/image-of-j-in-the-classical-adams-spectral-sequence Image of J in the classical Adams Spectral Sequence Joseph Victor 2012-09-03T19:29:55Z 2012-09-03T19:50:57Z <p>Hey all,</p> <p>I know that in some versions of the Adams Spectral Sequence you can easily identify the image of $J$, and I was wondering if there was a way to identify the image of $J$ in the $E_2$ page of the classical mod-2 version, especially for $t-s=3$ (mod 4). Since the order of this image is known and it is known that the image is a direct summand, it isn't so hard to find it in $E_\infty$. Of course, if you can identify $Im(J)$ in an earlier page, then you learn a huge amount about the differentials in that column. This might imply that identifying the image of $J$ is almost as hard as calculating the differentials, so maybe this is too much to hope for, but maybe just maybe there's a trick. </p> <p>Thanks</p> http://mathoverflow.net/questions/106268/image-of-j-in-the-classical-adams-spectral-sequence/106270#106270 Answer by Christian Nassau for Image of J in the classical Adams Spectral Sequence Christian Nassau 2012-09-03T19:50:57Z 2012-09-03T19:50:57Z <p>The image of $J$ is pretty easy to see in the Adams $E_2$ term: it consists of the elements along the vanishing line, plus, in dimensions 8k-1, of the towers that end near the vanishing line. </p> <p>This identification is due to Mahowald, see <em>The order of the image of the J-homomorphism</em> for the announcement ( <a href="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.bams/1183532412" rel="nofollow">http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.bams/1183532412</a> ) and <em>On bo-resolutions</em> ( <a href="http://projecteuclid.org/DPubS?verb=Display&amp;version=1.0&amp;service=UI&amp;handle=euclid.pjm/1102736799&amp;page=record" rel="nofollow">http://projecteuclid.org/DPubS?verb=Display&amp;version=1.0&amp;service=UI&amp;handle=euclid.pjm/1102736799&amp;page=record</a> ) for details.</p>