Titlebook: Cohomology Rings of Finite Groups; With an Appendix: Ca Jon F. Carlson,Lisa Townsley,Mucheng Zhang Book 2003 Springer Science+Business Medi

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Spectral Sequences,count of spectral sequences. Perhaps with some imagination the reader can guess how the pages of a spectral sequence of a filtered complex might unfold. We consider only first quadrant cohomology spectral sequences. Homology spectral sequences are similar in reasonably obvious ways. The spectral seq

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Cohomology Rings of Modules, ring H* (., .) via the isomorphism ., and the fact that Hom.(., .) is a finitely generated .-module. For this reason there exists a cohomological support variety ..(.) of the module . which is a subvariety of ..(.) and which reflects many of the homological properties of the module.

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Complexity and Multiple Complexes,he late 1970’s and it helped to motivate much of the development of the homological properties of modules. In fact, the complexity of a finitely generated .module . is a rather crude invariant, in that it only measures the polynomial rate of growth of a minimal projective resolution of the module. T

圓柱

Duality Complexes,es of a system of homogeneous parameters for the cohomology ring H* (.). Spectral sequences arise from truncated versions of the periodic complexes. In this chapter, we use the constructions to show that for any .-module ., the cohomology H.(.) can not equal zero for too many consecutive values of .

競(jìng)選運(yùn)動(dòng)

Transfers, Depth and Detection,ntinue to explore the properties of cohomology rings and the ensuing relationship to group structure. A principal focus is the detection of cohomology by subgroups of the given group. We would like to know if there is a collection of subgroups of a group such that kernels of the restriction maps to

結(jié)構(gòu)

Subgroup Complexes,group . of .. If . is not a .-group, extracting the cohomology of . as a subring of the cohomology ring of . is often a matter of finding the invariant elements. This reduces to an application of some sort of invariant theory. There must be some way of determining the action of the group on its .-su