Assembly maps in coarse geometry
Event details
| Date | 05.04.2016 |
| Hour | 10:15 › 11:30 |
| Speaker |
Matthew Gadsden (University of Sheffield) |
| Location |
CM113
|
| Category | Conferences - Seminars |
Coarse geometry is the study of large scale properties of spaces. In coarse geometry, two spaces are considered the same if they "behave the same at infinity", neglecting the fine detail which is important in topology. For example we consider the real numbers and the integers to be large-scale equivalent, as they look the same when you view them from far away. Although seemingly completely opposite to topology, many results and properties in topology have large-scale analogues in coarse geometry.
In geometric topology, a number of different maps are known as assembly maps, and various conjectures are present which say that these maps are injective under certain assumptions. The injectivity of these assembly maps give us geometric consequences which are of interest to many.
In this talk, I will introduce the area of coarse geometry and the concept of asymptotic dimension, and explain some of the links between this area and topology. I will give the framework required for a "universal" assembly map for finite asymptotic dimension which will apply to areas such as C*-algebra K-theory, algebraic K-theory and L-theory. A brief discussion of some of these areas will be given as applications for the main result.
In geometric topology, a number of different maps are known as assembly maps, and various conjectures are present which say that these maps are injective under certain assumptions. The injectivity of these assembly maps give us geometric consequences which are of interest to many.
In this talk, I will introduce the area of coarse geometry and the concept of asymptotic dimension, and explain some of the links between this area and topology. I will give the framework required for a "universal" assembly map for finite asymptotic dimension which will apply to areas such as C*-algebra K-theory, algebraic K-theory and L-theory. A brief discussion of some of these areas will be given as applications for the main result.
Links
Practical information
- Informed public
- Free
Organizer
- Magdalena Kedziorek