Casacuberta, CarlesAsensio Abella, Andrés2018-01-242018-01-242016-09-11https://hdl.handle.net/2445/119256Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2016, Director: Carles CasacubertaThe 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.73 p.application/pdfengcc-by-nc-nd (c) Andrés Asensio Abella, 2016http://creativecommons.org/licenses/by-nc-nd/3.0/es/K-teoriaEspais topològicsTreballs de fi de màsterAnells commutatiusK-theoryTopological spacesMaster's thesesinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess