A minimal set of generators for the cohomology is:
  • w1(r16) of degree 1
  • w4(r22) of degree 4
  • w1(r3) of degree 1
  • w2(r11) of degree 2
  • w of degree 3
The Steenrod operations are as follows:
  • Sq1(w4(r22)) = 0
  • Sq2(w4(r22)) = w4(r22)w2(r11)
  • Sq3(w4(r22)) = 0
  • Sq1(w2(r11)) = 0
  • Sq1(w) = 0
  • Sq2(w) = 0
Here is a minimal system of equations:
  • (1)          w1(r16)2 = 0
  • (2)          w1(r16)w1(r3) + w1(r3)2 = 0
  • (3)          w1(r16)w2(r11) = 0
  • (4)          w1(r16)w = 0
  • (5)          w2 = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r16)
  • w1(r2) = w1(r16) + w1(r3)
  • w1(r3) = w1(r3)
  • w2(r4) = 0
  • w2(r6) = w1(r16)w1(r3)
  • w2(r8) = w1(r16)w1(r3) + w2(r11)
  • w2(r9) = w1(r16)w1(r3) + w2(r11)
  • w2(r10) = w2(r11)
  • w2(r11) = w2(r11)
  • w1(r16) = w1(r16)
  • w2(r16) = w2(r11)
  • w4(r17) = w2(r11)2
  • w2(r18) = 0
  • w4(r18) = 0
  • w2(r20) = w2(r11)
  • w4(r20) = w4(r22)
  • w2(r21) = w2(r11)
  • w4(r21) = w4(r22)
  • w2(r22) = w2(r11)
  • w4(r22) = w4(r22)
  • w2(r23) = w2(r11)
  • w4(r23) = w4(r22)
Chern classes:
  • c1(r1) = 0
  • c1(r2) = w1(r16)w1(r3)
  • c1(r3) = w1(r16)w1(r3)
  • c1(r4) = 0
  • c1(r5) = 0
  • c1(r6) = w1(r16)w1(r3)
  • c1(r7) = w1(r16)w1(r3)
  • c1(r8) = w1(r16)w1(r3) + w2(r11)
  • c1(r9) = w1(r16)w1(r3) + w2(r11)
  • c1(r10) = w2(r11)
  • c1(r11) = w2(r11)
  • c1(r12) = w1(r16)w1(r3) + w2(r11)
  • c1(r13) = w1(r16)w1(r3) + w2(r11)
  • c1(r14) = w2(r11)
  • c1(r15) = w2(r11)
  • c1(r16) = 0
  • c2(r16) = w2(r11)2
  • c2(r17) = w2(r11)2
  • c1(r18) = 0
  • c2(r18) = 0
  • c1(r19) = 0
  • c2(r19) = 0
  • c1(r20) = w2(r11)
  • c2(r20) = w4(r22)
  • c1(r21) = w2(r11)
  • c2(r21) = w4(r22)
  • c1(r22) = w2(r11)
  • c2(r22) = w4(r22)
  • c1(r23) = w2(r11)
  • c2(r23) = w4(r22)
  • c1(r24) = w2(r11)
  • c2(r24) = w4(r22)
  • c1(r25) = w2(r11)
  • c2(r25) = w4(r22)
  • c1(r26) = w2(r11)
  • c2(r26) = w4(r22)
  • c1(r27) = w2(r11)
  • c2(r27) = w4(r22)
The results above have been produced during the second run in April, 2008.