Title: Towards the 3 line in Adams-Novikov spectralsequence
Abstract: The Adams-Novikov spectral sequence is very
important in algebraic topology, for calculating the stable
homotopy groups of spheres. We calculated Ext1 (M 1/2) and Ext0 (M
2/1), which are useful to calculate the 3 line of Adams-Novikov
spectral sequence. We first induced the long exact sequences
[formula does not render] by the short exact sequence [formula does
not render]. Then we divide elements in Ext0 (M 1/2) by v2 as many
times as possible, to achieve elements with a nontrivial images
under the map δ, which is related to the right unit ηR and the
coproduct Δ in the Hopf algebroid (BP*;BP* (BP)). Finally we check
the linear independence of the generators to calculate Ext1 (M
1/2). Then we do the analogical procedure for the long exact
sequence [formula does not render] induced by the short exact
sequence [formula does not render] to calculate Ext0 (M
2/1).
Publication Year: 2018
Publication Date: 2018-01-01
Language: en
Type: article
Access and Citation
Cited By Count: 1
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