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.
  • Dimension Theory and Separation Theorems from A History of Algebraic and Differential Topology, 1900-1969 by J. Dieudonné, Birkhäuser (1989
  • 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. 71, 169-175 (1912)
  • 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)