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The course will take place on Thursdays from 16:00 to 17:45 CET. Each lecture will consist of two 45-minute parts separated by a short break, and with some time for questions. A link with the recording of each lecture will be available a few days after each lecture.
- February 6th: Juan Rojo - Introduction to orbifolds in dimension 2 (I).
The content of the first two sessions will be the following.
Motivation: 2-orbifolds as quotient spaces.
Definition of 2-orbifolds.
Examples of non-quotient orbifolds (bad orbifolds).
Orientable and non-orientable 2-orbifolds.
Orbi-Euler characteristic, orbi-coverings.
Orbi-fundamental group: working definition and examples.
Orbi-metrics and Gauss-Bonnet.
Elliptic, parabollic and hyperbollic 2-orbifolds.
Classification of geometric 2-orbifolds. Orbi-tesselations.
Definition of n-dimensional orbifold: analogies and differences with 2-dimensions.
References:
Chapter 13 of the notes The geometry and topology of three manifolds, W. Thurston.
Chapter 2 of the notes Three dimensional orbifolds and their geometric structures, M. Boileau, S. Maillot, J. Porti.
Chapter 3.2.4 of Geometry and topology of manifolds: surfaces and beyond, V. Muñoz, A. González-Prieto, J. Rojo
- February 13th: Juan Rojo - Introduction to orbifolds in dimension 2 (II).
The content of the first two sessions will be the following.
Motivation: 2-orbifolds as quotient spaces.
Definition of 2-orbifolds.
Examples of non-quotient orbifolds (bad orbifolds).
Orientable and non-orientable 2-orbifolds.
Orbi-Euler characteristic, orbi-coverings.
Orbi-fundamental group: working definition and examples.
Orbi-metrics and Gauss-Bonnet.
Elliptic, parabollic and hyperbollic 2-orbifolds.
Classification of geometric 2-orbifolds. Orbi-tesselations.
Definition of n-dimensional orbifold: analogies and differences with 2-dimensions.
References:
Chapter 13 of the notes The geometry and topology of three manifolds, W. Thurston.
Chapter 2 of the notes Three dimensional orbifolds and their geometric structures, M. Boileau, S. Maillot, J. Porti.
Chapter 3.2.4 of Geometry and topology of manifolds: surfaces and beyond, V. Muñoz, A. González-Prieto, J. Rojo
- February 20th: Enrique Artal
The content of the sessions 3 and 4 will be the following.
Ramified covers and orbifold covers
Orbifold fundamental group
Orbifold covers
Seifert fibrations and locally trivial orbifold fibre bundles
Notes of the three lectures of Enrique Artal
- March 6th: Joan Porti - Orbifolds, branched coverings and knots.
- April 10th: Juan Rojo -
Abstract.
Organizers: Enrique Artal and Raquel Díaz | Contact address: radiaz@ucm.es
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