Homotopy Theory of Modules - Bleile, Beatrice
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Homological algebra generalizes the construction of (co-)homology theory of topological spaces, making it available for algebraic theories. In a similar vein, the homotopy theory of modules attempts to imitate topological homotopy theory. A discussion of the categorical notion of duality precedes the definition of the injective homotopy category. The absolute and relative homotopy groups are then defined and investigated. Finally, the homotopy groups of the cyclic group C_m are calculated for trivial C_m-modules.

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Produktbeschreibung
Homological algebra generalizes the construction of
(co-)homology theory of topological spaces, making it
available for algebraic theories. In a similar vein,
the homotopy theory of modules attempts to imitate
topological homotopy theory. A discussion of the
categorical notion of duality precedes the definition
of the injective homotopy category. The absolute and
relative homotopy groups are then defined and
investigated. Finally, the homotopy groups of the
cyclic group C_m are calculated for trivial C_m-modules.
Autorenporträt
Beatrice Bleile, Dipl.Math.ETH, PhD (University of Sydney),
Lecturer in Mathematics at the University of New England, NSW,
Australia.