A minimal set of generators for the cohomology is:
  • w2(r32) of degree 2
  • w2(r21) of degree 2
  • w1(r33) of degree 1
  • w1(r7) of degree 1
  • w2(r34) of degree 2
  • w1(r35) of degree 1
The Steenrod operations are as follows:
  • Sq1(w2(r32)) = w2(r32)w1(r33)
  • Sq1(w2(r21)) = 0
  • Sq1(w2(r34)) = w2(r32)w1(r33) + w1(r33)w2(r34) + w2(r32)w1(r35)
Here is a minimal system of equations:
  • (1)          w1(r33)2 + w1(r35)2 = 0
  • (2)          w1(r33)2 + w1(r33)w1(r35) = 0
  • (3)          w2(r32)w1(r33) + w1(r33)w2(r34) + w2(r32)w1(r35) + w2(r34)w1(r35) = 0
  • (4)          w2(r32)2 + w2(r34)2 = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r33) + w1(r35)
  • w1(r2) = w1(r35)
  • w1(r3) = w1(r33)
  • w1(r4) = w1(r33) + w1(r7)
  • w1(r5) = w1(r7) + w1(r35)
  • w1(r6) = w1(r33) + w1(r7) + w1(r35)
  • w1(r7) = w1(r7)
  • w2(r8) = 0
  • w2(r10) = w1(r33)2
  • w2(r12) = w1(r33)2 + w1(r7)2
  • w2(r14) = w1(r7)2
  • w2(r16) = w2(r21) + w1(r33)2 + w1(r7)2
  • w2(r17) = w2(r21) + w1(r33)2 + w1(r7)2
  • w2(r18) = w2(r21) + w1(r7)2
  • w2(r19) = w2(r21) + w1(r7)2
  • w2(r20) = w2(r21)
  • w2(r21) = w2(r21)
  • w2(r22) = w2(r21) + w1(r33)2
  • w2(r23) = w2(r21) + w1(r33)2
  • w1(r32) = w1(r33)
  • w2(r32) = w2(r32)
  • w1(r33) = w1(r33)
  • w2(r33) = w2(r32) + w1(r33)w1(r7) + w1(r7)2
  • w1(r34) = w1(r35)
  • w2(r34) = w2(r34)
  • w1(r35) = w1(r35)
  • w2(r35) = w1(r7)2 + w2(r34) + w1(r7)w1(r35)
  • w2(r36) = w1(r33)2
  • w4(r36) = w2(r32)2 + w2(r21)2 + w2(r21)w1(r33)2 + w1(r33)2w1(r7)2 + w1(r7)4
  • w2(r37) = w1(r33)2
  • w4(r37) = w2(r32)2 + w2(r21)2 + w2(r21)w1(r33)2
Chern classes:
  • c1(r1) = 0
  • c1(r2) = w1(r33)2
  • c1(r3) = w1(r33)2
  • c1(r4) = w1(r33)2 + w1(r7)2
  • c1(r5) = w1(r33)2 + w1(r7)2
  • c1(r6) = w1(r7)2
  • c1(r7) = w1(r7)2
  • c1(r8) = 0
  • c1(r9) = 0
  • c1(r10) = w1(r33)2
  • c1(r11) = w1(r33)2
  • c1(r12) = w1(r33)2 + w1(r7)2
  • c1(r13) = w1(r33)2 + w1(r7)2
  • c1(r14) = w1(r7)2
  • c1(r15) = w1(r7)2
  • c1(r16) = w2(r21) + w1(r33)2 + w1(r7)2
  • c1(r17) = w2(r21) + w1(r33)2 + w1(r7)2
  • c1(r18) = w2(r21) + w1(r7)2
  • c1(r19) = w2(r21) + w1(r7)2
  • c1(r20) = w2(r21)
  • c1(r21) = w2(r21)
  • c1(r22) = w2(r21) + w1(r33)2
  • c1(r23) = w2(r21) + w1(r33)2
  • c1(r24) = w2(r21) + w1(r33)2 + w1(r7)2
  • c1(r25) = w2(r21) + w1(r33)2 + w1(r7)2
  • c1(r26) = w2(r21) + w1(r7)2
  • c1(r27) = w2(r21) + w1(r7)2
  • c1(r28) = w2(r21)
  • c1(r29) = w2(r21)
  • c1(r30) = w2(r21) + w1(r33)2
  • c1(r31) = w2(r21) + w1(r33)2
  • c1(r32) = w1(r33)2
  • c2(r32) = w2(r32)2
  • c1(r33) = w1(r33)2
  • c2(r33) = w2(r32)2 + w1(r33)2w1(r7)2 + w1(r7)4
  • c1(r34) = w1(r33)2
  • c2(r34) = w2(r32)2
  • c1(r35) = w1(r33)2
  • c2(r35) = w2(r32)2 + w1(r33)2w1(r7)2 + w1(r7)4
  • c1(r36) = w1(r33)2
  • c2(r36) = w2(r32)2 + w2(r21)2 + w2(r21)w1(r33)2 + w1(r33)2w1(r7)2 + w1(r7)4
  • c1(r37) = w1(r33)2
  • c2(r37) = w2(r32)2 + w2(r21)2 + w2(r21)w1(r33)2
  • c1(r38) = w1(r33)2
  • c2(r38) = w2(r32)2 + w2(r21)2 + w2(r21)w1(r33)2 + w1(r33)2w1(r7)2 + w1(r7)4
  • c1(r39) = w1(r33)2
  • c2(r39) = w2(r32)2 + w2(r21)2 + w2(r21)w1(r33)2
The results above have been produced during the second run in April, 2008.