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General


Description

Classification of compact Riemann surfaces. Complex and geometric structures on compact surfaces. Teichmüller space. Coordinates on Teichmüller space.

Semester

Spring 2017 (Monday, January 23 to Friday, March 31)

Timetable

  • Mon 11:05 - 11:55

Prerequisites

Basic point set topology

Syllabus

The hyperbolic plane and hyperbolic geometry
Complex and hyperbolic structures on surfaces
Covering space theory for manifolds with extra structure
Uniformising theorems for simply connected surfaces with complex or hyperbolic structure.
Groups of holomorphic bijections. Covering groups of surfaces.
More on hyperbolic geometry. Geodesics, perpendiculars, polygons.
Hyperbolic structures on pairs of pants and compact surfaces with boundary.
Isotopy of loops and homeomorphisms. Ambient isotopy. Mapping class groups.
Teichmuller space. Coordinates, topology.

Lecturer


Mary Rees
Email maryrees@liverpool.ac.uk
Phone (0151) 7944063
vcard
Photo of Mary Rees


Students


Photo of John Blackman
John Blackman
(Durham)
Photo of Philip Carter
Philip Carter
(Liverpool)
Photo of Guillermo Cobos
Guillermo Cobos
(Durham)
Photo of Lorenzo De Biase
Lorenzo De Biase
(Cardiff)
Photo of Joe Driscoll
Joe Driscoll
(Leeds)
Photo of Massimo Gisonni
Massimo Gisonni
(Loughborough)
Photo of Thomas Honey
Thomas Honey
(Manchester)
Photo of Kunda Kambaso
Kunda Kambaso
(Durham)
Photo of Thomas Morley
Thomas Morley
(Sheffield)
Photo of Pedro Peres
Pedro Peres
(Exeter)
Photo of David Pescod
David Pescod
(Newcastle)
Photo of Matthew Poulter
Matthew Poulter
(Lancaster)
Photo of Sam Povall
Sam Povall
(Liverpool)
Photo of Jack Saunders
Jack Saunders
(Birmingham)
Photo of Albert Wood
Albert Wood
(*External)
Photo of Yiru Ye
Yiru Ye
(Loughborough)


Bibliography


Riemann Surfaces: A PrimerBeardon
A Primer on Riemann SurfacesBeardon
Lectures on Riemann SurfacesForster
Riemann SurfacesFarkas and Kra
Hyperbolic GeometryAnderson
Introduction to Hyperbolic GeometryRamsay and Richtmyer
Algebraic Topology BookHatcher
Topology And GeometryGlen E. Bredon
Automorphisms of Surfaces after Nielsen and ThurstonAndrew Casson and Stephen S. Bleiler
Hyperbolic GeometryIversen
An Introduction to Riemann Surfaces, Algebraic Curves and Moduli SpacesSchlichenmaier


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)

Assessment



Assessment will be by a take-home examination in the examination period 24 April -7 May. The examination will be available for viewing and download on 24 April. It is designed to completed in two hours by a student who has engaged with the course. the pass mark is 50 %

MAGIC028 Exam 2017

Files:Exam paper
Released: Monday 24 April 2017 (63.4 days ago)
Deadline: Sunday 7 May 2017 (49.4 days ago)


Recorded Lectures


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