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