Cocycle representatives in Ext(BP*) = ExtBP*(BP)s,t(BP*,BP*) at p=3

The table below is the E2 - term of the Adams-Novikov Spectral sequence at the prime 3. Each element of this E2 - term has a cocyle representative in the cobar complex. Clicking on an element in the E2 - term below will display its cocyle representative and other relevant information in the textbox below. A better picture of this E2 - term can be found on page 13 of Ravenel's book Complex Cobordism and the Homotopy Groups of Spheres (second edition). Detailed information about this E2 - term can be found in section 4.4 of Ravenel's book, and in Zahler's paper "The Adams-Novikov spectral sequence for the spheres" (Annals of Mathematics v.96 (1972), p.480-504) on page 501+. We use only the Araki generators and denote them by wi. We do not use the Hazewinkel generators, which we would denote by vi. These calculations were made using Maple, bigebra, and some tensor product procedures I wrote.


E2s,t = Ext(BP*) = ExtBP*(BP)s,t(BP*,BP*) at p=3:
s=9
s=8
s=7
s=6
s=5
s=4
s=3
s=2
s=1
s=0
t-s=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45


Here is a list of elements and cocycle representatives (products are not listed, since they are easily calculated: for example α_i β_j = α_i | β_j):
t-selementcocycle representativeother namesreference
3α1-8t_1h10Ravenel p.152
7α2 -16w_1t_1 + 192t_1^2
10β1-(t_1|t_1^2 + t_1^2|t_1)b1,0Ravenel p.123
11α3-24w_1^2t_1 + 576w_1t_1^2 - 4608t_1^3
34β3/3 -(3t_1|t_1^8 + 12t_1^2|t_1^7 + 28t_1^3|t_1^6 + 42t_1^4|t_1^5 + 42t_1^5|t_1^4 + 28t_1^6|t_1^3 + 12t_1^7|t_1^2 + 3t_1^8|t_1) b1,1Ravenel p.123