Higher order derived functors and the Adams spectral sequence |
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Authors: | Hans-Joachim Baues David Blanc |
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Institution: | 1. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany;2. Department of Mathematics, University of Haifa, 3498838 Haifa, Israel |
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Abstract: | Classical homological algebra studies chain complexes, resolutions, and derived functors in additive categories. In this paper we define higher order chain complexes, resolutions, and derived functors in the context of a new type of algebraic structure, called an algebra of left cubical balls . We show that higher order resolutions exist in these algebras, and that they determine higher order Ext-groups. In particular, the Em-term of the Adams spectral sequence (m>2) is such a higher Ext-group, providing a new way of constructing its differentials. |
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Keywords: | Primary 55T15 secondary 18G40 18G50 55S20 |
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