A minimal set of generators for the cohomology is:
  • w1(r6) of degree 1
  • w1(r7) of degree 1
  • w1(r5) of degree 1
  • w2(r45) of degree 2
The Steenrod operations are as follows:
  • Sq1(w2(r45)) = 0
Here is a minimal system of equations:
  • (1)          w1(r6)2 + w1(r7)2 = 0
Stiefel-Whitney classes:
  • w1(r1) = w1(r6) + w1(r7)
  • w1(r2) = w1(r7) + w1(r5)
  • w1(r3) = w1(r6) + w1(r5)
  • w1(r4) = w1(r6) + w1(r7) + w1(r5)
  • w1(r5) = w1(r5)
  • w1(r6) = w1(r6)
  • w1(r7) = w1(r7)
  • w2(r8) = 0
  • w2(r10) = w1(r6)2 + w1(r5)2
  • w2(r12) = w1(r5)2
  • w2(r14) = w1(r6)2
  • w2(r16) = 0
  • w2(r17) = 0
  • w2(r18) = w1(r6)2 + w1(r5)2
  • w2(r19) = w1(r6)2 + w1(r5)2
  • w2(r20) = w1(r5)2
  • w2(r21) = w1(r5)2
  • w2(r22) = w1(r6)2
  • w2(r23) = w1(r6)2
  • w2(r32) = w1(r5)2 + w2(r45)
  • w2(r33) = w1(r5)2 + w2(r45)
  • w2(r34) = w1(r6)2 + w2(r45)
  • w2(r35) = w1(r6)2 + w2(r45)
  • w2(r36) = w2(r45)
  • w2(r37) = w2(r45)
  • w2(r38) = w1(r6)2 + w1(r5)2 + w2(r45)
  • w2(r39) = w1(r6)2 + w1(r5)2 + w2(r45)
  • w2(r40) = w1(r5)2 + w2(r45)
  • w2(r41) = w1(r5)2 + w2(r45)
  • w2(r42) = w1(r6)2 + w2(r45)
  • w2(r43) = w1(r6)2 + w2(r45)
  • w2(r44) = w2(r45)
  • w2(r45) = w2(r45)
  • w2(r46) = w1(r6)2 + w1(r5)2 + w2(r45)
  • w2(r47) = w1(r6)2 + w1(r5)2 + w2(r45)
Chern classes:
  • c1(r1) = 0
  • c1(r2) = w1(r6)2 + w1(r5)2
  • c1(r3) = w1(r6)2 + w1(r5)2
  • c1(r4) = w1(r5)2
  • c1(r5) = w1(r5)2
  • c1(r6) = w1(r6)2
  • c1(r7) = w1(r6)2
  • c1(r8) = 0
  • c1(r9) = 0
  • c1(r10) = w1(r6)2 + w1(r5)2
  • c1(r11) = w1(r6)2 + w1(r5)2
  • c1(r12) = w1(r5)2
  • c1(r13) = w1(r5)2
  • c1(r14) = w1(r6)2
  • c1(r15) = w1(r6)2
  • c1(r16) = 0
  • c1(r17) = 0
  • c1(r18) = w1(r6)2 + w1(r5)2
  • c1(r19) = w1(r6)2 + w1(r5)2
  • c1(r20) = w1(r5)2
  • c1(r21) = w1(r5)2
  • c1(r22) = w1(r6)2
  • c1(r23) = w1(r6)2
  • c1(r24) = 0
  • c1(r25) = 0
  • c1(r26) = w1(r6)2 + w1(r5)2
  • c1(r27) = w1(r6)2 + w1(r5)2
  • c1(r28) = w1(r5)2
  • c1(r29) = w1(r5)2
  • c1(r30) = w1(r6)2
  • c1(r31) = w1(r6)2
  • c1(r32) = w1(r5)2 + w2(r45)
  • c1(r33) = w1(r5)2 + w2(r45)
  • c1(r34) = w1(r6)2 + w2(r45)
  • c1(r35) = w1(r6)2 + w2(r45)
  • c1(r36) = w2(r45)
  • c1(r37) = w2(r45)
  • c1(r38) = w1(r6)2 + w1(r5)2 + w2(r45)
  • c1(r39) = w1(r6)2 + w1(r5)2 + w2(r45)
  • c1(r40) = w1(r5)2 + w2(r45)
  • c1(r41) = w1(r5)2 + w2(r45)
  • c1(r42) = w1(r6)2 + w2(r45)
  • c1(r43) = w1(r6)2 + w2(r45)
  • c1(r44) = w2(r45)
  • c1(r45) = w2(r45)
  • c1(r46) = w1(r6)2 + w1(r5)2 + w2(r45)
  • c1(r47) = w1(r6)2 + w1(r5)2 + w2(r45)
  • c1(r48) = w1(r5)2 + w2(r45)
  • c1(r49) = w1(r5)2 + w2(r45)
  • c1(r50) = w1(r6)2 + w2(r45)
  • c1(r51) = w1(r6)2 + w2(r45)
  • c1(r52) = w2(r45)
  • c1(r53) = w2(r45)
  • c1(r54) = w1(r6)2 + w1(r5)2 + w2(r45)
  • c1(r55) = w1(r6)2 + w1(r5)2 + w2(r45)
  • c1(r56) = w1(r5)2 + w2(r45)
  • c1(r57) = w1(r5)2 + w2(r45)
  • c1(r58) = w1(r6)2 + w2(r45)
  • c1(r59) = w1(r6)2 + w2(r45)
  • c1(r60) = w2(r45)
  • c1(r61) = w2(r45)
  • c1(r62) = w1(r6)2 + w1(r5)2 + w2(r45)
  • c1(r63) = w1(r6)2 + w1(r5)2 + w2(r45)
The algebra of Milnor constants is generated by:
  • c1(r4) + c1(r32)
  • c1(r2) + c1(r4)
  • c1(r4)
  • Note: the only algebraic cycles in the cohomology are Chern classes.
The results above have been produced during the second run in April, 2008.