A minimal set of generators for the cohomology is:
  • w1(r13) of degree 1
  • w2(r16) of degree 2
  • w2(r10) of degree 2
  • w1(r9) of degree 1
  • w1(r11) of degree 1
  • w2(r13) of degree 2
The Steenrod operations are as follows:
  • Sq1(w2(r16)) = w2(r16)w1(r9)
  • Sq1(w2(r10)) = w2(r10)w1(r11)
  • Sq1(w2(r13)) = w1(r13)w2(r13)
Here is a minimal system of equations:
  • (1)          w1(r13)w1(r9) + w1(r9)2 + w1(r13)w1(r11) + w1(r11)2 = 0
  • (2)          w1(r13)2 + w1(r9)2 + w1(r13)w1(r11) + w1(r9)w1(r11) = 0
  • (3)          w1(r13)w2(r10) + w2(r10)w1(r9) + w2(r10)w1(r11) + w1(r13)w2(r13) + w1(r9)w2(r13) + w1(r11)w2(r13) = 0
  • (4)          w1(r13)2w2(r10) + w2(r10)2 + w1(r13)w2(r10)w1(r11) + w1(r13)w1(r9)w2(r13) + w1(r9)2w2(r13) + w2(r13)2 = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r13) + w1(r9) + w1(r11)
  • w1(r2) = w1(r13) + w1(r11)
  • w1(r3) = w1(r9)
  • w1(r4) = w1(r13) + w1(r9)
  • w1(r5) = w1(r11)
  • w1(r6) = w1(r9) + w1(r11)
  • w1(r7) = w1(r13)
  • w1(r8) = w1(r9)
  • w2(r8) = 0
  • w1(r9) = w1(r9)
  • w2(r9) = w1(r13)2 + w1(r13)w1(r9)
  • w1(r10) = w1(r11)
  • w2(r10) = w2(r10)
  • w1(r11) = w1(r11)
  • w2(r11) = w1(r13)2 + w2(r10) + w1(r13)w1(r11)
  • w1(r12) = w1(r13)
  • w2(r12) = w1(r13)w1(r9) + w1(r9)2 + w2(r13)
  • w1(r13) = w1(r13)
  • w2(r13) = w2(r13)
  • w1(r14) = w1(r9)
  • w2(r14) = w1(r13)2 + w2(r16) + w1(r13)w1(r9)
  • w1(r15) = w1(r9)
  • w2(r15) = w1(r13)2 + w2(r16) + w1(r13)w1(r9)
  • w1(r16) = w1(r9)
  • w2(r16) = w2(r16)
  • w1(r17) = w1(r9)
  • w2(r17) = w2(r16)
  • w1(r18) = 0
  • w2(r18) = w1(r13)2 + w1(r13)w1(r9) + w1(r9)2
  • w3(r18) = w1(r13)2w1(r9) + w1(r13)w1(r9)2
  • w4(r18) = w1(r13)2w2(r16) + w2(r16)2 + w1(r13)2w2(r10) + w2(r10)2 + w1(r13)w2(r16)w1(r9) + w1(r13)w2(r10)w1(r11)
Chern classes:
  • c1(r1) = w1(r13)2 + w1(r13)w1(r9) + w1(r13)w1(r11)
  • c1(r2) = w1(r13)2 + w1(r13)w1(r9) + w1(r9)2 + w1(r13)w1(r11)
  • c1(r3) = w1(r9)2
  • c1(r4) = w1(r13)2 + w1(r9)2
  • c1(r5) = w1(r13)w1(r9) + w1(r9)2 + w1(r13)w1(r11)
  • c1(r6) = w1(r13)w1(r9) + w1(r13)w1(r11)
  • c1(r7) = w1(r13)2
  • c1(r8) = w1(r9)2
  • c2(r8) = 0
  • c1(r9) = w1(r9)2
  • c2(r9) = w1(r13)4 + w1(r13)2w1(r9)2
  • c1(r10) = w1(r13)w1(r9) + w1(r9)2 + w1(r13)w1(r11)
  • c2(r10) = w2(r10)2
  • c1(r11) = w1(r13)w1(r9) + w1(r9)2 + w1(r13)w1(r11)
  • c2(r11) = w1(r13)4 + w2(r10)2 + w1(r13)3w1(r9) + w1(r13)2w1(r9)2 + w1(r13)3w1(r11)
  • c1(r12) = w1(r13)2
  • c2(r12) = w1(r13)2w2(r10) + w2(r10)2 + w1(r13)2w1(r9)2 + w1(r9)4 + w1(r13)w2(r10)w1(r11) + w1(r13)w1(r9)w2(r13) + w1(r9)2w2(r13)
  • c1(r13) = w1(r13)2
  • c2(r13) = w1(r13)2w2(r10) + w2(r10)2 + w1(r13)w2(r10)w1(r11) + w1(r13)w1(r9)w2(r13) + w1(r9)2w2(r13)
  • c1(r14) = w1(r9)2
  • c2(r14) = w1(r13)4 + w2(r16)2 + w1(r13)2w1(r9)2
  • c1(r15) = w1(r9)2
  • c2(r15) = w1(r13)4 + w2(r16)2 + w1(r13)2w1(r9)2
  • c1(r16) = w1(r9)2
  • c2(r16) = w2(r16)2
  • c1(r17) = w1(r9)2
  • c2(r17) = w2(r16)2
  • c1(r18) = 0
  • c2(r18) = w1(r13)4 + w1(r13)2w1(r9)2 + w1(r9)4
  • c3(r18) = w1(r13)4w1(r9)2 + w1(r13)2w1(r9)4
  • c4(r18) = w1(r13)4w2(r16)2 + w2(r16)4 + w1(r13)4w2(r10)2 + w2(r10)4 + w1(r13)3w2(r10)2w1(r9) + w1(r13)2w2(r16)2w1(r9)2 + w1(r13)2w2(r10)2w1(r9)2 + w1(r13)3w2(r10)2w1(r11)
The results above have been produced during the second run in April, 2008.