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