A minimal set of generators for the cohomology is:
  • w1(r15) of degree 1
  • w1(r11) of degree 1
  • w1(r13) of degree 1
  • w2(r44) of degree 2
  • w1(r14) of degree 1
  • w2(r56) of degree 2
The Steenrod operations are as follows:
  • Sq1(w2(r44)) = 0
  • Sq1(w2(r56)) = 0
Here is a minimal system of equations:
  • (1)          w1(r15)2 + w1(r14)2 = 0
  • (2)          w1(r15)2 + w1(r13)2 = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r15) + w1(r14)
  • w1(r2) = w1(r15) + w1(r13)
  • w1(r3) = w1(r13) + w1(r14)
  • w1(r4) = w1(r15) + w1(r11)
  • w1(r5) = w1(r11) + w1(r14)
  • w1(r6) = w1(r11) + w1(r13)
  • w1(r7) = w1(r15) + w1(r11) + w1(r13) + w1(r14)
  • w1(r8) = w1(r11) + w1(r13) + w1(r14)
  • w1(r9) = w1(r15) + w1(r11) + w1(r13)
  • w1(r10) = w1(r15) + w1(r11) + w1(r14)
  • w1(r11) = w1(r11)
  • w1(r12) = w1(r15) + w1(r13) + w1(r14)
  • w1(r13) = w1(r13)
  • w1(r14) = w1(r14)
  • w1(r15) = w1(r15)
  • w2(r16) = w1(r15)2 + w1(r11)2 + w2(r44) + w2(r56)
  • w2(r18) = w1(r15)2 + w1(r11)2 + w2(r44) + w2(r56)
  • w2(r20) = w2(r44) + w2(r56)
  • w2(r22) = w2(r44) + w2(r56)
  • w2(r24) = w1(r15)2 + w2(r44) + w2(r56)
  • w2(r26) = w1(r15)2 + w2(r44) + w2(r56)
  • w2(r28) = w1(r11)2 + w2(r44) + w2(r56)
  • w2(r30) = w1(r11)2 + w2(r44) + w2(r56)
  • w2(r32) = w1(r15)2 + w2(r44)
  • w2(r33) = w1(r15)2 + w2(r44)
  • w2(r36) = w1(r11)2 + w2(r44)
  • w2(r37) = w1(r11)2 + w2(r44)
  • w2(r40) = w1(r15)2 + w1(r11)2 + w2(r44)
  • w2(r41) = w1(r15)2 + w1(r11)2 + w2(r44)
  • w2(r44) = w2(r44)
  • w2(r45) = w2(r44)
  • w2(r48) = w1(r11)2 + w2(r56)
  • w2(r49) = w1(r11)2 + w2(r56)
  • w2(r52) = w1(r15)2 + w2(r56)
  • w2(r53) = w1(r15)2 + w2(r56)
  • w2(r56) = w2(r56)
  • w2(r57) = w2(r56)
  • w2(r60) = w1(r15)2 + w1(r11)2 + w2(r56)
  • w2(r61) = w1(r15)2 + w1(r11)2 + w2(r56)
Chern classes:
  • c1(r1) = 0
  • c1(r2) = 0
  • c1(r3) = 0
  • c1(r4) = w1(r15)2 + w1(r11)2
  • c1(r5) = w1(r15)2 + w1(r11)2
  • c1(r6) = w1(r15)2 + w1(r11)2
  • c1(r7) = w1(r15)2 + w1(r11)2
  • c1(r8) = w1(r11)2
  • c1(r9) = w1(r11)2
  • c1(r10) = w1(r11)2
  • c1(r11) = w1(r11)2
  • c1(r12) = w1(r15)2
  • c1(r13) = w1(r15)2
  • c1(r14) = w1(r15)2
  • c1(r15) = w1(r15)2
  • c1(r16) = w1(r15)2 + w1(r11)2 + w2(r44) + w2(r56)
  • c1(r17) = w1(r15)2 + w1(r11)2 + w2(r44) + w2(r56)
  • c1(r18) = w1(r15)2 + w1(r11)2 + w2(r44) + w2(r56)
  • c1(r19) = w1(r15)2 + w1(r11)2 + w2(r44) + w2(r56)
  • c1(r20) = w2(r44) + w2(r56)
  • c1(r21) = w2(r44) + w2(r56)
  • c1(r22) = w2(r44) + w2(r56)
  • c1(r23) = w2(r44) + w2(r56)
  • c1(r24) = w1(r15)2 + w2(r44) + w2(r56)
  • c1(r25) = w1(r15)2 + w2(r44) + w2(r56)
  • c1(r26) = w1(r15)2 + w2(r44) + w2(r56)
  • c1(r27) = w1(r15)2 + w2(r44) + w2(r56)
  • c1(r28) = w1(r11)2 + w2(r44) + w2(r56)
  • c1(r29) = w1(r11)2 + w2(r44) + w2(r56)
  • c1(r30) = w1(r11)2 + w2(r44) + w2(r56)
  • c1(r31) = w1(r11)2 + w2(r44) + w2(r56)
  • c1(r32) = w1(r15)2 + w2(r44)
  • c1(r33) = w1(r15)2 + w2(r44)
  • c1(r34) = w1(r15)2 + w2(r44)
  • c1(r35) = w1(r15)2 + w2(r44)
  • c1(r36) = w1(r11)2 + w2(r44)
  • c1(r37) = w1(r11)2 + w2(r44)
  • c1(r38) = w1(r11)2 + w2(r44)
  • c1(r39) = w1(r11)2 + w2(r44)
  • c1(r40) = w1(r15)2 + w1(r11)2 + w2(r44)
  • c1(r41) = w1(r15)2 + w1(r11)2 + w2(r44)
  • c1(r42) = w1(r15)2 + w1(r11)2 + w2(r44)
  • c1(r43) = w1(r15)2 + w1(r11)2 + w2(r44)
  • c1(r44) = w2(r44)
  • c1(r45) = w2(r44)
  • c1(r46) = w2(r44)
  • c1(r47) = w2(r44)
  • c1(r48) = w1(r11)2 + w2(r56)
  • c1(r49) = w1(r11)2 + w2(r56)
  • c1(r50) = w1(r11)2 + w2(r56)
  • c1(r51) = w1(r11)2 + w2(r56)
  • c1(r52) = w1(r15)2 + w2(r56)
  • c1(r53) = w1(r15)2 + w2(r56)
  • c1(r54) = w1(r15)2 + w2(r56)
  • c1(r55) = w1(r15)2 + w2(r56)
  • c1(r56) = w2(r56)
  • c1(r57) = w2(r56)
  • c1(r58) = w2(r56)
  • c1(r59) = w2(r56)
  • c1(r60) = w1(r15)2 + w1(r11)2 + w2(r56)
  • c1(r61) = w1(r15)2 + w1(r11)2 + w2(r56)
  • c1(r62) = w1(r15)2 + w1(r11)2 + w2(r56)
  • c1(r63) = w1(r15)2 + w1(r11)2 + w2(r56)
The algebra of Milnor constants is generated by:
  • c1(r4) + c1(r8) + c1(r32)
  • c1(r8) + c1(r16) + c1(r32)
  • w1(r15)w1(r13) + w1(r15)w1(r14) + w1(r13)w1(r14) + w1(r14)2 which is not a combination of Chern classes; it is nilpotent of order 2
  • c1(r8)
  • c1(r4) + c1(r8)
The results above have been produced during the second run in April, 2008.