Algebraic topology of embedded submanifolds
| Thesis title in Czech: | Algebraická topologie vnořených podvariet |
|---|---|
| Thesis title in English: | Algebraic topology of embedded submanifolds |
| Key words: | charakteristické třídy|singulární kohomologie|normální bundle vnořené podvariety|Schubertův kalkulus|zobecněná vlajková varieta |
| English key words: | characteristic classes|singular cohomology|generalized flag manifold|normal bundle of embedded submanifold|Schubert calculus |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | doc. RNDr. Petr Somberg, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 20.01.2025 |
| Date of assignment: | 20.01.2025 |
| Confirmed by Study dept. on: | 20.01.2025 |
| Date of electronic submission: | 27.04.2025 |
| Date of submission of printed version: | 27.04.2025 |
| Opponents: | doc. RNDr. Jiří Vanžura, CSc. |
| Guidelines |
| The theme of magister thesis is a topological characterization
of normal bundles of embedded submanifolds, a topic on the intersection of algebraic topology, geometry (both algebraic and differential) and representation theory. A prototype example is given by the embedded smaller rank Grassmann manifold in a higher rank Grassmann manifold, equipped with (compatible) Bruhat cell decomposition, Schubert calculus and the structure of generalized flag manifold. The aim is to rely on several mutually related tools, e.g. singular cohomology theory and K-theory as well as representation theory of Lie resp. Weyl groups, to give some description of normal bundles in terms of characteristic classes, representation theory, etc. |
| References |
| Chriss, Ginzburg: Representation Theory and Complex Geometry,
B. Kostant and S. Kumar, T-equivariant K-theory of generalized flag varieties S.L. Kleiman, D. Laksov, Schubert calculus |
| Preliminary scope of work in English |
| The theme of magister thesis is a topological characterization
of normal bundles of embedded submanifolds, a topic on the intersection of algebraic topology, geometry (both algebraic and differential) and representation theory. A prototype example is given by the embedded smaller rank Grassmann manifold in a higher rank Grassmann manifold, equipped with (compatible) Bruhat cell decomposition, Schubert calculus and the structure of generalized flag manifold. The aim is to rely on several mutually related tools, e.g. singular cohomology theory and K-theory as well as representation theory of Lie resp. Weyl groups, to give some description of normal bundles in terms of characteristic classes, representation theory, etc. |