A minimal set of generators for the cohomology is:
  • w1(r11) of degree 1
  • w1(r14) of degree 1
  • w1(r13) of degree 1
  • w2(r19) of degree 2
  • w1(r15) of degree 1
  • w2(r21) of degree 2
The Steenrod operations are as follows:
  • Sq1(w2(r19)) = w1(r11)w2(r19) + w1(r14)w2(r19)
  • Sq1(w2(r21)) = w1(r11)w2(r21)
Here is a minimal system of equations:
  • (1)          w1(r11)w1(r13) + w1(r13)2 + w1(r11)w1(r15) + w1(r15)2 = 0
  • (2)          w1(r11)w1(r14) + w1(r11)w1(r13) + w1(r13)2 + w1(r14)w1(r15) = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r14) + w1(r15)
  • w1(r2) = w1(r13) + w1(r15)
  • w1(r3) = w1(r14) + w1(r13)
  • w1(r4) = w1(r11) + w1(r15)
  • w1(r5) = w1(r11) + w1(r14)
  • w1(r6) = w1(r11) + w1(r13)
  • w1(r7) = w1(r11) + w1(r14) + w1(r13) + w1(r15)
  • w1(r8) = w1(r11) + w1(r14) + w1(r13)
  • w1(r9) = w1(r11) + w1(r13) + w1(r15)
  • w1(r10) = w1(r11) + w1(r14) + w1(r15)
  • w1(r11) = w1(r11)
  • w1(r12) = w1(r14) + w1(r13) + w1(r15)
  • w1(r13) = w1(r13)
  • w1(r14) = w1(r14)
  • w1(r15) = w1(r15)
  • w1(r16) = w1(r11) + w1(r14)
  • w2(r16) = w1(r11)w1(r14) + w2(r19)
  • w1(r17) = w1(r11) + w1(r14)
  • w2(r17) = w1(r11)w1(r13) + w1(r14)w1(r13) + w1(r13)2 + w2(r19)
  • w1(r18) = w1(r11) + w1(r14)
  • w2(r18) = w1(r11)w1(r14) + w1(r11)w1(r13) + w1(r14)w1(r13) + w1(r13)2 + w2(r19)
  • w1(r19) = w1(r11) + w1(r14)
  • w2(r19) = w2(r19)
  • w1(r20) = w1(r11)
  • w2(r20) = w1(r11)w1(r14) + w1(r14)2 + w1(r11)w1(r13) + w1(r13)2 + w2(r21)
  • w1(r21) = w1(r11)
  • w2(r21) = w2(r21)
  • w1(r22) = w1(r11)
  • w2(r22) = w1(r11)w1(r14) + w1(r14)2 + w2(r21)
  • w1(r23) = w1(r11)
  • w2(r23) = w1(r11)w1(r13) + w1(r13)2 + w2(r21)
  • w1(r24) = 0
  • w2(r24) = w1(r11)2 + w1(r11)w1(r14) + w1(r14)2
  • w3(r24) = w1(r11)2w1(r14) + w1(r11)w1(r14)2
  • w4(r24) = w1(r11)w1(r14)w2(r19) + w2(r19)2 + w1(r11)w1(r14)w2(r21) + w1(r14)2w2(r21) + w2(r21)2
Chern classes:
  • c1(r1) = w1(r14)2 + w1(r11)w1(r13) + w1(r13)2 + w1(r11)w1(r15)
  • c1(r2) = w1(r11)w1(r13) + w1(r11)w1(r15)
  • c1(r3) = w1(r14)2 + w1(r13)2
  • c1(r4) = w1(r11)2 + w1(r11)w1(r13) + w1(r13)2 + w1(r11)w1(r15)
  • c1(r5) = w1(r11)2 + w1(r14)2
  • c1(r6) = w1(r11)2 + w1(r13)2
  • c1(r7) = w1(r11)2 + w1(r14)2 + w1(r11)w1(r13) + w1(r11)w1(r15)
  • c1(r8) = w1(r11)2 + w1(r14)2 + w1(r13)2
  • c1(r9) = w1(r11)2 + w1(r11)w1(r13) + w1(r11)w1(r15)
  • c1(r10) = w1(r11)2 + w1(r14)2 + w1(r11)w1(r13) + w1(r13)2 + w1(r11)w1(r15)
  • c1(r11) = w1(r11)2
  • c1(r12) = w1(r14)2 + w1(r11)w1(r13) + w1(r11)w1(r15)
  • c1(r13) = w1(r13)2
  • c1(r14) = w1(r14)2
  • c1(r15) = w1(r11)w1(r13) + w1(r13)2 + w1(r11)w1(r15)
  • c1(r16) = w1(r11)2 + w1(r14)2
  • c2(r16) = w1(r11)2w1(r14)2 + w2(r19)2
  • c1(r17) = w1(r11)2 + w1(r14)2
  • c2(r17) = w1(r11)2w1(r14)w1(r13) + w1(r11)w1(r14)2w1(r13) + w1(r11)w1(r14)w1(r13)2 + w2(r19)2
  • c1(r18) = w1(r11)2 + w1(r14)2
  • c2(r18) = w1(r11)2w1(r14)2 + w1(r11)2w1(r14)w1(r13) + w1(r11)w1(r14)2w1(r13) + w1(r11)w1(r14)w1(r13)2 + w2(r19)2
  • c1(r19) = w1(r11)2 + w1(r14)2
  • c2(r19) = w2(r19)2
  • c1(r20) = w1(r11)2
  • c2(r20) = w1(r11)2w1(r14)2 + w1(r14)4 + w1(r11)2w1(r14)w1(r13) + w1(r11)w1(r14)2w1(r13) + w1(r11)w1(r14)w1(r13)2 + w1(r14)2w1(r13)2 + w2(r21)2
  • c1(r21) = w1(r11)2
  • c2(r21) = w2(r21)2
  • c1(r22) = w1(r11)2
  • c2(r22) = w1(r11)2w1(r14)2 + w1(r14)4 + w2(r21)2
  • c1(r23) = w1(r11)2
  • c2(r23) = w1(r11)2w1(r14)w1(r13) + w1(r11)w1(r14)2w1(r13) + w1(r11)w1(r14)w1(r13)2 + w1(r14)2w1(r13)2 + w2(r21)2
  • c1(r24) = 0
  • c2(r24) = w1(r11)4 + w1(r11)2w1(r14)2 + w1(r14)4
  • c3(r24) = w1(r11)4w1(r14)2 + w1(r11)2w1(r14)4
  • c4(r24) = w1(r11)2w1(r14)2w2(r19)2 + w2(r19)4 + w1(r11)2w1(r14)2w2(r21)2 + w1(r14)4w2(r21)2 + w2(r21)4
The results above have been produced during the second run in April, 2008.