A minimal set of generators for the cohomology is:
  • w1(r7) of degree 1
  • w2(r14) of degree 2
  • w1(r17) of degree 1
  • w4(r22) of degree 4
  • w1(r5) of degree 1
  • v of degree 3
The Steenrod operations are as follows:
  • Sq1(w2(r14)) = 0
  • Sq1(w4(r22)) = 0
  • Sq2(w4(r22)) = w1(r7)2w4(r22) + w2(r14)w4(r22) + w1(r7)w1(r17)w4(r22) + w1(r17)w4(r22)w1(r5)
  • Sq3(w4(r22)) = 0
  • Sq1(v) = 0
  • Sq2(v) = 0
Here is a minimal system of equations:
  • (1)          w1(r17)2 = 0
  • (2)          w1(r7)2 + w1(r7)w1(r17) + w1(r17)w1(r5) + w1(r5)2 = 0
  • (3)          w1(r7)2w1(r17) + w2(r14)w1(r17) = 0
  • (4)          w1(r17)v = 0
  • (5)          w1(r7)6 + w1(r7)4w2(r14) + w1(r7)2w2(r14)2 + w2(r14)3 + v2 = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r17)
  • w1(r2) = w1(r7) + w1(r5)
  • w1(r3) = w1(r7) + w1(r17) + w1(r5)
  • w1(r4) = w1(r17) + w1(r5)
  • w1(r5) = w1(r5)
  • w1(r6) = w1(r7) + w1(r17)
  • w1(r7) = w1(r7)
  • w2(r8) = w1(r7)2 + w2(r14)
  • w2(r10) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • w2(r12) = w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • w2(r14) = w2(r14)
  • w1(r16) = w1(r17)
  • w2(r16) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • w1(r17) = w1(r17)
  • w2(r17) = w2(r14) + w1(r17)w1(r5)
  • w4(r18) = 0
  • w4(r19) = w1(r7)4
  • w2(r20) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • w4(r20) = w1(r7)2w2(r14) + w1(r7)3w1(r17) + w4(r22) + w1(r7)2w1(r17)w1(r5)
  • w2(r21) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • w4(r21) = w1(r7)2w2(r14) + w1(r7)3w1(r17) + w4(r22) + w1(r7)2w1(r17)w1(r5)
  • w2(r22) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • w4(r22) = w4(r22)
  • w2(r23) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • w4(r23) = w4(r22)
Chern classes:
  • c1(r1) = 0
  • c1(r2) = w1(r7)w1(r17) + w1(r17)w1(r5)
  • c1(r3) = w1(r7)w1(r17) + w1(r17)w1(r5)
  • c1(r4) = w1(r7)2 + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c1(r5) = w1(r7)2 + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c1(r6) = w1(r7)2
  • c1(r7) = w1(r7)2
  • c1(r8) = w1(r7)2 + w2(r14)
  • c1(r9) = w1(r7)2 + w2(r14)
  • c1(r10) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c1(r11) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c1(r12) = w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c1(r13) = w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c1(r14) = w2(r14)
  • c1(r15) = w2(r14)
  • c1(r16) = 0
  • c2(r16) = w1(r7)4 + w2(r14)2
  • c1(r17) = 0
  • c2(r17) = w2(r14)2
  • c2(r18) = 0
  • c2(r19) = w1(r7)4
  • c1(r20) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c2(r20) = w1(r7)2w2(r14) + w1(r7)3w1(r17) + w4(r22) + w1(r7)2w1(r17)w1(r5)
  • c1(r21) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c2(r21) = w1(r7)2w2(r14) + w1(r7)3w1(r17) + w4(r22) + w1(r7)2w1(r17)w1(r5)
  • c1(r22) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c2(r22) = w4(r22)
  • c1(r23) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c2(r23) = w4(r22)
  • c1(r24) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c2(r24) = w1(r7)2w2(r14) + w1(r7)3w1(r17) + w4(r22) + w1(r7)2w1(r17)w1(r5)
  • c1(r25) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c2(r25) = w1(r7)2w2(r14) + w1(r7)3w1(r17) + w4(r22) + w1(r7)2w1(r17)w1(r5)
  • c1(r26) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c2(r26) = w4(r22)
  • c1(r27) = w1(r7)2 + w2(r14) + w1(r7)w1(r17) + w1(r17)w1(r5)
  • c2(r27) = w4(r22)
The results above have been produced during the second run in April, 2008.