On the cohomology of split extensions

Benson, D. J.; Feshbach, M.

doi:10.1090/S0002-9939-1994-1186129-9

On the cohomology of split extensions
HTML articles powered by AMS MathViewer

by D. J. Benson and M. Feshbach

Proc. Amer. Math. Soc. 121 (1994), 687-690

DOI: https://doi.org/10.1090/S0002-9939-1994-1186129-9

PDF | Request permission

Abstract:

We construct, for each value of n, a split extension of finite 2-groups, with complement isomorphic to Z/2 , for which the differential ${d_n}$ is nonzero in the Lyndon-Hochschild-Serre spectral sequence.

References

George S. Avrunin and Jon F. Carlson, Nilpotency degree of cohomology rings in characteristic two, Proc. Amer. Math. Soc. 118 (1993), no. 2, 339–343. MR 1129871, DOI 10.1090/S0002-9939-1993-1129871-7
D. J. Benson, Representations and cohomology. II, Cambridge Studies in Advanced Mathematics, vol. 31, Cambridge University Press, Cambridge, 1991. Cohomology of groups and modules. MR 1156302
Mark Feshbach, The image of $H^{\ast } (BG,\,\textbf {Z})$ in $H^{\ast } (BT,\,\textbf {Z})$ for $G$ a compact Lie group with maximal torus $T$, Topology 20 (1981), no. 1, 93–95. MR 592571, DOI 10.1016/0040-9383(81)90015-X
Daniel Quillen, The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. (2) 94 (1971), 549–572; ibid. (2) 94 (1971), 573–602. MR 298694, DOI 10.2307/1970770
Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, Graduate Texts in Mathematics, Vol. 29, Springer-Verlag, New York-Heidelberg, 1975. Reprint of the 1960 edition. MR 0389876