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


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


  • Mon 11:05 - 11:55


Basic point set topology


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.


Mary Rees
Phone (0151) 7944063
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Photo of John Blackman
John Blackman
Photo of Philip Carter
Philip Carter
Photo of Guillermo Cobos
Guillermo Cobos
Photo of Lorenzo De Biase
Lorenzo De Biase
Photo of Joe Driscoll
Joe Driscoll
Photo of Massimo Gisonni
Massimo Gisonni
Photo of Thomas Honey
Thomas Honey
Photo of Kunda Kambaso
Kunda Kambaso
Photo of Thomas Morley
Thomas Morley
Photo of Pedro Peres
Pedro Peres
Photo of David Pescod
David Pescod
Photo of Matthew Poulter
Matthew Poulter
Photo of Sam Povall
Sam Povall
Photo of Jack Saunders
Jack Saunders
Photo of Albert Wood
Albert Wood
Photo of Yiru Ye
Yiru Ye


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


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 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 (333.6 days ago)
Deadline: Sunday 7 May 2017 (319.6 days ago)

Recorded Lectures

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