MATS4200 Alexandrov spaces (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2017-2018, 2018-2019, 2019-2020
Description
Content
The course is intended as an introduction to Alexandrov spaces with curvature bounded below. We will go through
•Definitions and examples of Alexandrov spaces with curvature bounded below
•Toponogov's theorem (local-to-global property)
•Maximal diameter and splitting theorems
•Bishop-Gromov inequality and Gromov's precompactness theorem
•Strainers and local geometry of Alexandrov spaces
Completion methods
One can complete the course either by:
•Exercises and course exam or
•Final exam
Learning outcomes
After completing the course the student will
•Understand the definitions of curvature lower bounds in the sense of Alexandrov and can check in easy examples if they are satisfied
•Know the basic ideas behind the proofs of the main theorems presented in the course.
•Understand the definitions of curvature lower bounds in the sense of Alexandrov and can check in easy examples if they are satisfied
•Know the basic ideas behind the proofs of the main theorems presented in the course.
Description of prerequisites
The following courses are preferred but not obligatory
•MATS213 Metric Spaces
•MATS331 Metric Geometry
•MATS111 Measure and Integration Theory 1
•MATS112 Measure and Integration Theory 2
•MATS213 Metric Spaces
•MATS331 Metric Geometry
•MATS111 Measure and Integration Theory 1
•MATS112 Measure and Integration Theory 2
Study materials
S. Alexander, V.Kapovitch, A. Petrunin, Alexandrov Geometry (draft available at http://anton-petrunin.github.io/book/all.pdf )
D. Burago, Y. Burago, S. Ivanov: A Course in Metric Geometry, American Mathematical Society, 2001.
D. Burago, Y. Burago, S. Ivanov: A Course in Metric Geometry, American Mathematical Society, 2001.
Completion methods
Method 1
Select all marked parts
Parts of the completion methods
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Unpublished assessment item