Apol, D. (2021) Representability of Cohomology Theories on CW-complexes. Bachelor's Thesis, Mathematics.
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Abstract
In topology, it is in general very difficult to decide whether or not two spaces are homotopy equivalent. In algebraic topology, therefore, algebraic invariants are associated with each space, reflecting some topological data. Examples of this are homology and cohomology, that originated from measuring the number and size of holes in topological spaces. They turn out to be versatile and related to much that is cared about in algebraic topology. In this thesis, we will show that, as long as we restrict ourselves to a certain subclass of topological spaces, namely that of CW-complexes, all cohomology theories are representable by a sequence of CW-complexes. To do so, we first explore singular homology and cohomology, define what generalised cohomology theories are, and use the homotopy theory of CW-complexes to prove this main result.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Veen, R.I. van der and Lorscheid, O. and Becerra Garrido, J. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 12 Jul 2021 08:38 |
| Last Modified: | 12 Jul 2021 08:38 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/25152 |
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