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