Место издания:Cornell University Libtary Ithaca, New York
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Последняя страница:41
Аннотация:We study simplicial profinite groups with a view towards applications in profinite combinatorial group theory. This approach provides a natural framework to the concept of pro-C-presentation of a pro-C-group G as a 1-truncation of its free simplicial pro-C-resolution. The category of simplicial pro-C-groups has a closed simplicial model category structure. This yields a possibility to define some old and new derived functors as left Quillen derived functors from this simplicial model category. When C is L-groups, than may construct free simplical pro-L-resolution functorially. We introduce settings of Δ-adic and Zassenhaus filtrations for free simplical pro-p-resolutions and derive some calculations for pro-p-groups. The usage of pro-p-Curtis-Rector spectral sequences sheds homotopical light on Golod-Shafarevitch type results.
