By Jon F. Carlson, L. Townsley, Luís Valero-Elizondo, Mucheng Zhang
Workforce cohomology has a wealthy historical past that is going again a century or extra. Its origins are rooted in investigations of staff conception and num ber thought, and it grew into an imperative element of algebraic topology. within the final thirty years, workforce cohomology has constructed a robust con nection with finite workforce representations. not like the early functions that have been basically concerned about cohomology in low levels, the in teractions with illustration conception contain cohomology earrings and the geometry of spectra over those jewelry. it really is this connection to represen tation concept that we take as our basic motivation for this publication. The publication involves separate items. Chronologically, the 1st half was once the pc calculations of the mod-2 cohomology earrings of the teams whose orders divide sixty four. the information and the courses for the calculations have been constructed during the last 10 years. numerous new positive aspects have been further over the process that point. We had initially deliberate to incorporate just a short creation to the calculations. in spite of the fact that, we have been persuaded to provide a extra large textual content that might contain in better element the innovations which are the topic of the calculations and are the resource of a few of the motivating conjectures for the com putations. now we have accumulated jointly the various effects and ideas which are the focal point of the calculations from through the mathematical literature.
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