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| dc.contributor | Casacuberta, Carles | |
| dc.creator | Asensio Abella, Andrés | |
| dc.date | 2018-01-24T11:26:17Z | |
| dc.date | 2018-01-24T11:26:17Z | |
| dc.date | 2016-09-11 | |
| dc.date.accessioned | 2024-12-16T10:26:05Z | |
| dc.date.available | 2024-12-16T10:26:05Z | |
| dc.identifier | http://hdl.handle.net/2445/119256 | |
| dc.identifier.uri | http://fima-docencia.ub.edu:8080/xmlui/handle/123456789/20496 | |
| dc.description | Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2016, Director: Carles Casacuberta | |
| dc.description | 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. | |
| dc.format | 73 p. | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.rights | cc-by-nc-nd (c) Andrés Asensio Abella, 2016 | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.source | Màster Oficial - Matemàtica Avançada | |
| dc.subject | K-teoria | |
| dc.subject | Espais topològics | |
| dc.subject | Treballs de fi de màster | |
| dc.subject | Anells commutatius | |
| dc.subject | K-theory | |
| dc.subject | Topological spaces | |
| dc.subject | Master's theses | |
| dc.title | Acyclicity in Algebraic K-theory | |
| dc.type | info:eu-repo/semantics/masterThesis |
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