Homotopy classification of graded Picard categories

• Autores: Antonio M. Cegarra, Emzar Khmaladze
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 213, Nº 2, 2007, págs. 644-686
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.01.015
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• Resumen

  • Certain low-dimensional symmetric cohomology groups of G-modules, for any given group G, are computed as the cohomology of an explicit cochain complex. This result is used to establish natural one-to-one correspondences between elements of the 3rd symmetric cohomology groups of G-modules, G-equivariant pointed 2-connected homotopy 4-types, and equivalence classes of G-graded Picard categories. The simplicial nerve of a G-graded Picard category is also constructed and studied.