Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/119256
Acyclicity in Algebraic K-theory
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The central topic of this work is the concept of acyclic spaces in topological K-theory and their analogues in algebraic K-theory. We start by describing topological K-theory and some basic results, such as representability by a spectrum. Next we discuss algebraic K-theory and some of its properties, including Swan’s theorem, followed by the topological tools required to construct higher algebraic K-theory by means of
Quillen’s plus-construction. Finally, we describe a class of rings whose algebraic K-theory groups vanish in all dimensions. In fact each ring $R$ admits a cone $CR$ with $K_i (CR) = 0$ for all i and a suspension $SR$ that is used to define negative K-theory groups of R in analogy with the topological case.
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Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2016, Director: Carles Casacuberta
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ASENSIO ABELLA, Andrés. Acyclicity in Algebraic K-theory. [consulted: 7 of October of 2026]. Available at: https://hdl.handle.net/2445/119256