A minimal set of generators for the cohomology is:
  • w2(r6) of degree 2
  • w1(r17) of degree 1
  • w1(r3) of degree 1
  • w2(r16) of degree 2
The Steenrod operations are as follows:
  • Sq1(w2(r6)) = 0
  • Sq1(w2(r16)) = w1(r17)w2(r16)
Here is a minimal system of equations:
  • (1)          w1(r17)2 = 0
  • (2)          w1(r17)w1(r3) + w1(r3)2 = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r17)
  • w1(r2) = w1(r17) + w1(r3)
  • w1(r3) = w1(r3)
  • w2(r4) = w2(r6) + w1(r17)w1(r3)
  • w2(r6) = w2(r6)
  • w1(r8) = w1(r17)
  • w2(r8) = 0
  • w4(r9) = w2(r6)2
  • w1(r10) = w1(r17)
  • w2(r10) = 0
  • w1(r11) = w1(r17)
  • w2(r11) = 0
  • w4(r12) = w2(r6)2
  • w4(r13) = w2(r6)2
  • w1(r14) = w1(r17)
  • w2(r14) = w2(r16)
  • w1(r15) = w1(r17)
  • w2(r15) = w2(r16)
  • w1(r16) = w1(r17)
  • w2(r16) = w2(r16)
  • w1(r17) = w1(r17)
  • w2(r17) = w2(r16)
  • w4(r18) = w2(r6)2 + w2(r16)2
  • w4(r19) = w2(r6)2 + w2(r16)2
  • w4(r20) = w2(r6)2 + w2(r16)2
  • w4(r21) = w2(r6)2 + w2(r16)2
Chern classes:
  • c1(r1) = 0
  • c1(r2) = w1(r17)w1(r3)
  • c1(r3) = w1(r17)w1(r3)
  • c1(r4) = w2(r6) + w1(r17)w1(r3)
  • c1(r5) = w2(r6) + w1(r17)w1(r3)
  • c1(r6) = w2(r6)
  • c1(r7) = w2(r6)
  • c1(r8) = 0
  • c2(r8) = 0
  • c2(r9) = w2(r6)2
  • c1(r10) = 0
  • c2(r10) = 0
  • c1(r11) = 0
  • c2(r11) = 0
  • c2(r12) = w2(r6)2
  • c2(r13) = w2(r6)2
  • c1(r14) = 0
  • c2(r14) = w2(r16)2
  • c1(r15) = 0
  • c2(r15) = w2(r16)2
  • c1(r16) = 0
  • c2(r16) = w2(r16)2
  • c1(r17) = 0
  • c2(r17) = w2(r16)2
  • c2(r18) = w2(r6)2 + w2(r16)2
  • c2(r19) = w2(r6)2 + w2(r16)2
  • c2(r20) = w2(r6)2 + w2(r16)2
  • c2(r21) = w2(r6)2 + w2(r16)2
The algebra of Milnor constants is generated by:
  • c1(r2) + c1(r4)
  • c1(r2)
  • c2(r14)
  • w1(r17)w1(r3)w2(r16) which is not a combination of Chern classes; it is nilpotent of order 2
The results above have been produced during the second run in April, 2008.