A minimal set of generators for the cohomology is:
  • w1(r8) of degree 1
  • w2(r8) of degree 2
  • w1(r3) of degree 1
  • w4(r10) of degree 4
  • w of degree 3
The Steenrod operations are as follows:
  • Sq1(w2(r8)) = 0
  • Sq1(w4(r10)) = 0
  • Sq2(w4(r10)) = w2(r8)w4(r10)
  • Sq3(w4(r10)) = 0
  • Sq1(w) = 0
  • Sq2(w) = 0
Here is a minimal system of equations:
  • (1)          w1(r8)2 = 0
  • (2)          w1(r8)w1(r3) + w1(r3)2 = 0
  • (3)          w1(r8)w2(r8) = 0
  • (4)          w1(r8)w = 0
  • (5)          w2(r8)3 + w2 = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r8)
  • w1(r2) = w1(r8) + w1(r3)
  • w1(r3) = w1(r3)
  • w2(r4) = w2(r8) + w1(r8)w1(r3)
  • w2(r6) = w2(r8)
  • w1(r8) = w1(r8)
  • w2(r8) = w2(r8)
  • w4(r9) = 0
  • w2(r10) = w2(r8)
  • w4(r10) = w4(r10)
  • w2(r11) = w2(r8)
  • w4(r11) = w4(r10)
Chern classes:
  • c1(r1) = 0
  • c1(r2) = w1(r8)w1(r3)
  • c1(r3) = w1(r8)w1(r3)
  • c1(r4) = w2(r8) + w1(r8)w1(r3)
  • c1(r5) = w2(r8) + w1(r8)w1(r3)
  • c1(r6) = w2(r8)
  • c1(r7) = w2(r8)
  • c1(r8) = 0
  • c2(r8) = w2(r8)2
  • c2(r9) = 0
  • c1(r10) = w2(r8)
  • c2(r10) = w4(r10)
  • c1(r11) = w2(r8)
  • c2(r11) = w4(r10)
  • c1(r12) = w2(r8)
  • c2(r12) = w4(r10)
  • c1(r13) = w2(r8)
  • c2(r13) = w4(r10)
The results above have been produced during the second run in April, 2008.