Summer @ Icerm 2018 Material

Below are suggestions, reading material, interesting blogs or people to read from, compiled in the SUMER@ICERM program.




Here is the list of problems to think about in Moira’s lecture (thanks Rob for writing them down). This is a paper that contains a parametrization of all pair of pants, useful for Groups 1 and 2.

In this link you’ll find a great app (coded by Matt Genkin) draw “unrolled” pair of pants on the Poincare disk, and parts of geodesics. 

Here are good crochet instructions (there are also many videos on youtube. If you find a good one, let me know and I’ll post it here). The handout is here

Below is a list of possibly useful material for the summer related to surfaces and closed curves on surfaces.

A paper where a parametrization of all hyperbolic pair of pants is described.

Cinderella is a lady who lost her shoe, and a wonderful program to draw geometric objects.

Slides of my talk about hyperbolic geometry and about problems 1 and 2.

The preliminary list of problems.

A very basic introduction to topology of curves and surfaces 

Mostly surfaces by Richard Schwartz. You can also find here for an earlier draft of the book, provided by the author. (Advised reading: 

  • Chapter 2: Defintion of a  Surface (specially 2.7)
  •  Chapther 3: The glueing construction (specially  3.3 The Classification of Surfaces and 3.4 The Euler Characteristic)
  • Chapter 4: The fundamental group (concentrate on surfaces)
  • Chapter 5. Examples of fundamental groups (concentrate on surfaces)
  • Chapter 6 Covering Spaces and the Deck Group
  • Chapter 10 Hyperbolic Geometry
  • Chapter 12: Hyperbolic Surfaces)

An introduction to hyperbolic geometry by Cannon, Floyd, Kenyon and Parry.

Another introduction to hyperbolic geometry, by Walkden. (In page 134 you’ll find the definition of limit set)

 A primer on mapping class groups by Benson Farb and Dan Margalit, Chapters 1, 2 and 3.

Nice pictures of different models of the hyperbolic plane here.


Topology of surfaces by Christine Kinsey, Chapter 4, 5, and 9.

A basic introduction to the Goldman bracket  by me, Moira Chas.

Anderson's book "Hyperbolic geometry”, 

Mumford-Series-Wright's "Indra's Pearls" .

Ratcliffe's book "Hyperbolic manifolds” is another text on hyperbolic geometry.

Rachel Zhang’s paper clearly explains (among other things) the concept of linked pairs that yields an algorithm to compute intersection and self-intersection of deformation classes of curves on a surface with boundary (when the curves are described in terms of the words on the generators of the fundamental group)

Beginning topology, Sue E. Godman.

 Relations between word length, hyperbolic length and self-intersection numbers of curves on surfaces by me, Moira Chas.

Low-dimensional geometry, from Euclidean surfaces to hyperbolic knots, by Francis Bonahon, the first five chapters. 

Here is a link that implements the algorithm to compute the Goldman bracket of two free homotopy classes of closed curves on a surface with boundary. (It “kind of” works for closed surfaces, although the final answer is not in its most reduced form)

This article, by Tony Phillips, explains ideas about curvature. You can use it to compute the curvature of crocheted hyperbolic planes.