Curves on Surfaces

Some (mostly on-line) resources

W.Abikoff , "The uniformization theorem"

Introduction to topology:

A. Katok, A. Sossinsky, Introduction to Modern Topology and Geometry , ---- (Chapter 5, Topology and Geometry of surfaces).
E.C.Zeeman, Introduction to Topology. The Classification theorem for Surfaces,, ---- (with nice pictures).

Some books:

R.C.Penner, J.L.Harer, "Combinatorics of train tracks", Chapter 1. Princeton, N.J. : Princeton University Press, 1992.
R.C.Penner, "Decorated Teichmüller theory", Zürich : European Mathematical Society, 2012.
B.Farb, D.Margalit, "A primer on mapping class groups"
C.Series, "Hyperbolic geometry"
M.Kapovich, "Hyperbolic Manifolds and Discrete Groups"

Teichmüller Theory:

M.Kapovich, "Introduction to Teichmüller Theory"

Pants Decompositions:

A. Hatcher, Pants decompositions. ----

Curve Complex:

S. Schleimer, Notes on the complex of curves,. ----
Y.N.Minsky, Curve complexes, surfaces and 3-manifolds, ---- survey.
L. Ji, Curve complexes versus Tits buildings: structures and applications . ----

Triangulations and Laminations:

A.Hatcher, On triangulations of surfaces. ----
A.Hatcher, Measured lamination spaces for surfaces, from the topological viewpoint. ----
V.V.Fock, A.B.Goncharov, Dual Teichmuller and lamination spaces. ----
S.Fomin, M.Shapiro, D.Thurston, Cluster algebras and triangulated surfaces. Part I: cluster complexes. ----

Heegaard splittings:

Jesse Johnson, Notes on Heegaard splittings . ----
Martin Scharlemann, Heegaard splittings of 3-manifolds. ----

Billiards:

Serge Tabachnikov, Geometry and Billiards . ----
Anton Zorich, Flat geometry on Riemann surfaces and Teichmuller dynamics in moduli spaces . ----
Rebecca Lehman, Chad White, Hyperbolic billiard paths . ----
Filiz Dogru, Serge Tabachnikov, Dual billiard . ----
Filiz Dogru, Serge Tabachnikov, On polygonal dual billiard in the hyperbolic plane . ----
Simon Castle, Norbert Peyerimhoff, Karl Friedrich Siburg, Billiards in ideal hyperbolic polygons . ----

Dimer models:

Raf Bocklandt, A Dimer ABC . ----

Curve lengths:

Sara Maloni, Caroline Series, Top terms of polynomial traces in Kra's plumbing construction .
Dylan Thurston, Geometric intersection of curves on surfaces .
Sara Maloni, Frederic Palesi, Ser Peow Tan, On the character variety of the hour-holed sphere.
Francis Bonahon, Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form.
Francois Gueritaud, On canonical triangulations of once-punctured torus bundles and two-bridge link complements (with appendix A by David Futer).
Lee Mosher, A user's guide to the mapping class group: once punctured surfaces.

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There are also lecture notes for the graduate course "Curves on Surfaces" by Dylan Thurston ---- (not an easy reading!)