The Classification of Surfaces
and the Jordan Curve Theorem
Secondary literature
Surfaces (Wikipedia article)
The Jordan curve theorem (Wikipedia article)
MathOverflow
discussion of the triangulation of surfaces.
Manifold Atlas Project
Analysis Situs French website on Poincare and topology.
Dimension Theory and Separation Theorems
from A History of Algebraic and Differential Topology, 1900-1969 by J. Dieudonné, Birkhäuser (1989)
The evolution of the concept of homeomorphism bg Gregory H. Moore, Historia Mathematica 34, 333--343 (2007)
The Classification Theorem for Compact Surfaces,
Jean Gallier and Dianna Xu. Book in progress (2011).
The classification of surfaces Andrew Ranicki,
slides for SMSTC lecture (24 November, 2011). Previous lectures:
Coverings and the Galois correspondence Vanya Cheltsov (17 November, 2011),
The Seifert-van Kampen theorem Andrew Ranicki (10 November, 2011),
The fundamental group and covering spaces Vanya Cheltsov (3 November, 2011).
MacTutor entries for A.F.Möbius
(1790-1868) ,
C.Jordan (1838-1922).
Google
for the Jordan Curve Theorem
Google
for the classification of surfaces
Letter from Larry Siebenmann about the
Jordan Curve Theorem (2005)
Primary literature
Vorstudien zur Topologie
by J.B.Listing, Göttinger Studien 1, 811--875 (1847)
Memoire sur la theorie generale des surfaces
by O.Bonnet, J. de l'Ecole Polytechnique 32, 1--146 (1849)
Theorie der Abel'schen Functionen
by B. Riemann, Borchardt's Journal für Reine und Angew. Math. 54, 81--135 (1857)
Der Census räumlicher Complexe
oder Verallgemeinerung des Euler'schen Satzes von der Polyedern,
by J.B. Listing, Abh. der Konigl. Ges. der Wiss. Göttingen 10,
1--86 (1862)
On Contour and Slope Lines A. Cayley,
The Philosophical Magazine 18 (120), 264--268 (1859)
Theorie der elementaren Verwandschaften A. Möbius, Abh. der Kön.
Sächsische Ges. der Wiss. 15, 18-57 (1863)
Sur la deformation des surfaces C. Jordan, J. de math. pures 11, 105-109 (1866)
Über diejenigen ebenen Curven, deren Coordinaten rationale Functionen eines Parameters
sind. by A. Clebsch, Borchardt's Journal für die reine und angewandte
Mathematik 64, 43--65 (1865)
On Hills and Dales by James Clerk Maxwell,
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 4th Series,
40(269):421--425, December 1870.
Extract
from A Treatise on Electricity and Magnetism by James Clerk Maxwell (OUP 1873).
An essentially topological account of Stokes' theorem, using the
first (cyclomatic) and second (periphractic) Betti numbers,
and Poincaré-Lefschetz duality for surfaces with boundary,
as described in
Electromagnetic Theory and Computation: A Topological Approach by P.W.Gross and P.R.Kotiuga (MSRI/CUP 2001).
See also Iron Rings, Doctor Honoris Causa
Raoul Bott, and a Hidden Hand by P.R.Kotiuga (2010)
On the canonical form and dissection of a Riemann's surface,
W. K. Clifford, Proc. L.M.S. VIII, 292-304 (1877)
Beiträge zur Analysis Situs W. Dyck, Mat. Ann. 37, 457-512 (1888)
The original proof of the
Jordan Curve Theorem C. Jordan, Cours d'analyse (1887)
Poincaré's papers on topology. English translation (2009) by
John Stillwell,
which are published
by the American Mathematical Society.
Theory on plane curves in nonmetrical
analysis situs O. Veblen, Trans. A.M.S. 6, 83-98 (1905)
Analysis Situs
M. Dehn and P. Heegaard, Enzykl der Math. Wiss. III.1, 153-220 (1907)
Beweis des Jordanschen Kurvensatzes
L.E.J. Brouwer, Math. Ann. 69, 169-175 (1911)
A proof of Jordan's Theorem about a simple
closed curve J.W. Alexander, Annals of Math. 21, 180-184
(1920)
Systems of circuits on two-dimensional
manifolds H.R. Brahana, Ann. of Maths. (2) 23, 144--168 (1921)
A proof and extension of the Jordan-Brouwer
Separation Theorem J.W. Alexander, Trans. A.M.S. 23, 333-349
(1922)
Über den Begriff der Riemannschen Fläche,
T. Rado, Acta Sc. Math. (Szeged) 2, 101--121 (1924)
Vorlesungen über Topologie
B. Kerékjértó, Springer (1925)
The Jordan Curve Theorem for Polygons, Extract from What is Mathematics?
(OUP, 1941, 2nd ed. 1996) by R. Courant and H. Robbins.
Introduction to topology E.C.Zeeman, Warwick notes (1966)
The Jordan curve theorem and an unpublished manuscript by
Max Dehn H. Guggenheimer, Arch. Hist. Exact Sci. 17, 193-200 (1977)
The Jordan curve theorem revisited Dost\'al M. and Tindell R., Jahresber. Deutsch.
Math.-Verein, 80, 111--128 (1978)
A proof of the Jordan curve theorem
H. Tverberg, Bull. London Math. Soc. 12, 34-38 (1980)
Camille Jordan et les Fondements de
l'Analyse Orsay Ph.D. thesis of H. Gispert-Chambaz (1982)
The Jordan Curve Theorem via the Brouwer
Fixed Point Theorem
R. Maehara, Amer. Math. Month. 91, 641--643 (1984)
Classification of Surfaces
C.E.Burgess, Amer. Math. Month. 92, 349--354 (1985)
The classification of surfaces, Peter Andrews, Amer. Math. Month. 95, 861--867 (1988)
The Jordan-Schoenflies Theorem
and the Classification of Surfaces
C. Thomassen, Amer. Math. Month. 99, 116--131 (1992)
The Jordan Curve Theorem for Polygons An algorithmic proof,
O. Cismasu (1997)
A nonstandard proof of the Jordan Curve Theorem by V.Kanovei and M.Reeken, Real. An. Exch. 24,
161--169 (1999/9)
Conway's ZIP proof of the classification of surfaces.
G. Francis and J. Weeks. Amer. Math. Month. 106, 393--399 (1999)
Groupoids, the Phragmen-Brouwer Property,
and the Jordan Curve Theorem
A proof of the Jordan Curve Theorem using the van Kampen theorem for the fundamental
groupoid, R. Brown, J. Homotopy and Related Structures 1, 175--183 (2006)
Corrigendum (2014)
Jordan's proof of the Jordan curve theorem
T.C.Hales, Studies in Logic, Grammar and Rhetoric 10, 45-60(2007)
The Jordan curve theorem formally and informally
T.C.Hales, Amer. Math. Monthly 114, 882--894 (2007)
Formal proof T.C.Hales, Notices AMS 55, 1370--1380 (2008)
The Jordan curve theorem is nontrivial F. and W.T. Ross, J. Mathematics and the Arts (2009)
On the Jordan-Schoenflies theorem
notes on talk of M.Scharlemann (2013)