| 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 |
|