MATS4100 Introduction to Geometric Group Theory (3 op)
Opinnon taso:
Syventävät opinnot
Arviointiasteikko:
0-5
Suorituskieli:
englanti
Vastuuorganisaatio:
Matematiikan ja tilastotieteen laitos
Opetussuunnitelmakaudet:
2017-2018, 2018-2019, 2019-2020
Kuvaus
Sisältö
•Fundamental group, covering map, universal cover.
•Group action by isometries, finitely generated group, Cayley graph.
•Geometric action, Svarc-Milnor Lemma.
•The growth of a group, volume growth of a manifold, Gromov's theorem on polynomial growth.
•Hyperbolic space and manifold, Gromov hyperbolic metric spaces and groups.
•Amenable groups and the Banach Tarski paradox.
Suoritustavat
To pass the course, each student is required to present a problem on the board during the exercise sessions and to take the written exam
Osaamistavoitteet
•Become familiar with some of the objects/groups studied in Geometric Group Theory: finitely generated groups, Cayley graphs, isometric action on metric spaces.
•Understand geometric actions and their genericity (Svarc-Milnor Lemma)
•Understand some connections between Group Theory and Geometry, e.g. the importance of the fundamental group of a manifold, etc.
•Learn some of the comparison tools of Coarse Geometry: Lipschitz map, bi-Lipschitz equivalence, quasi-isometric map, quasi-isometry, etc.
•Become familiar with some of the most important theorems of GGT.
•Understand geometric actions and their genericity (Svarc-Milnor Lemma)
•Understand some connections between Group Theory and Geometry, e.g. the importance of the fundamental group of a manifold, etc.
•Learn some of the comparison tools of Coarse Geometry: Lipschitz map, bi-Lipschitz equivalence, quasi-isometric map, quasi-isometry, etc.
•Become familiar with some of the most important theorems of GGT.
Esitietojen kuvaus
Metric spaces, Algebra 1: Rings and Fields and Algebra 1: Groups
Suoritustavat
Tapa 1
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Osallistuminen opetukseen (3 op)
Tyyppi:
Osallistuminen opetukseen
Arviointiasteikko:
0-5
Suorituskieli:
englanti