Contents Introduction by D. J. Benson and F. R. Cohen 1 Artin's Braid Group and the Homology of Certain Subgroups of the Mapping Class Group by F. R. Cohen 6 1 Statement of Results 6 2 Presentations 8 3 H*(Kn Z) 9 4 Proof of Theorem 1.1 13 5 The mod-5 Cohomology of | 0 and 0 14 6 The mod-3 Cohomology of r^'0 . . . .' 15 7 The mod-2 Cohomology of T2 0 Theorems 1.3 and 1.4 16 8 H*(J:6]H*(Ke F5)) Theorem 5.3 18 9 Theorem 1.6 21 10 Facts about Bn and Lemmas 3.2 and 3.3 24 Specht Modules and the Cohomology of Mapping Class Groups by D. J. Benson 29 1 Introduction 29 2 The modules W(Kn,Z), j 3 36 3 Modules for Ae and He in characteristic two 40 4 Diagrams for i/-7(/6,F2) as F2*46-modules 47 5 Calculation of tf*(£6, H* (K6, F2)) = H*(T6Q0,F2) 61 6 Finite subgroups of TQQ and r 2 0 73 7 Calculation of the spectral sequences for/f*(ro 0 ,F 2 ) a n d / f * ( r 2 0 , F 2 ) 75 8 Calculations in characteristic three 78 The mod 2 cohomology of the mapping class group for a surface of genus two by D. J. Benson and F. R. Cohe n 93 1 Introduction 93 2 A construction for K(TQQ, 1) characteristic classes 94 3 Steenrod operations on H*(F(S2,6)/E6,F2) 99 4 Steenrod operations on i7*(ro 0 ,F 2 ) 100 5 The spectral sequence for T2 0 102 iii
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