Editing Surface (topology) (section)

==References==
*{{Citation | first = Walther | last = Dyck | author-link = Walther von Dyck | title = Beiträge zur Analysis situs I | journal = Math. Ann. | volume = 32 | year = 1888 | issue = 4 | pages = 459–512 | doi=10.1007/bf01443580| s2cid = 118123073 }}

===Simplicial proofs of classification up to homeomorphism===
*{{citation|last1= Seifert|first1= Herbert|last2= Threlfall|first2= William|title= A textbook of topology|series= Pure and Applied Mathematics|volume= 89|publisher= Academic Press|year= 1980|isbn= 0126348502|url-access= registration|url= https://archive.org/details/seifertthrelfall0000seif}}, English translation of 1934 classic German textbook
*{{citation|last1= Ahlfors|first1= Lars V.|last2= Sario|first2= Leo|title=Riemann surfaces|series=Princeton Mathematical Series|volume= 26|publisher= Princeton University Press|year= 1960}}, Chapter I
*{{citation|last=Maunder|first=C. R. F.|title= Algebraic topology|publisher= Dover Publications|year=1996|isbn= 0486691314}}, Cambridge undergraduate course
*{{cite book| author=Massey, William S.| title=A Basic Course in Algebraic Topology| publisher=Springer-Verlag| year=1991| isbn= 0-387-97430-X}}
*{{cite book| author=Bredon, Glen E.|author-link = Glen Bredon| title=Topology and Geometry| publisher=Springer-Verlag| year=1993| isbn= 0-387-97926-3}}
*{{citation|last=Jost|first= Jürgen|title=Compact Riemann surfaces: an introduction to contemporary mathematics|edition=3rd|publisher=Springer|year=2006|isbn=3540330658}}, for closed oriented [[Riemannian manifold]]s

===Morse theoretic proofs of classification up to diffeomorphism===
*{{citation|first=M.|last=Hirsch|title=Differential topology|year=1994|edition=2nd|publisher=Springer}}
*{{citation|last= Gauld|first= David B.|title= Differential topology: an introduction|series= Monographs and Textbooks in Pure and Applied Mathematics|volume= 72|publisher= Marcel Dekker|year= 1982|isbn= 0824717090|url-access= registration|url= https://archive.org/details/differentialtopo0000gaul}}
*{{citation|last=Shastri|first=Anant R. |title=Elements of differential topology|publisher= CRC Press|year=2011|isbn= 9781439831601}}, careful proof aimed at undergraduates
*{{cite book| author= Gramain, André|title=Topology of Surfaces| publisher=BCS Associates| year=1984|isbn = 0-914351-01-X}} [http://www.math.u-psud.fr/~biblio/numerisation/docs/G_GRAMAIN-55/pdf/G_GRAMAIN-55.pdf (Original 1969-70 Orsay course notes in French for "Topologie des Surfaces")]
*{{citation | author=A. Champanerkar|title=Classification of surfaces via Morse Theory|url=http://www.math.csi.cuny.edu/abhijit/papers/classification.pdf | postscript=, an exposition of Gramain's notes|display-authors=etal}}

===Other proofs===
*{{citation|first=Terry |last=Lawson|title=Topology: a geometric approach|publisher=Oxford University Press|isbn=0-19-851597-9|year=2003}}, similar to Morse theoretic proof using sliding of attached handles
*{{citation | title = Conway's ZIP Proof | first1 = George K. | last1 = Francis | first2 = Jeffrey R. | last2 = Weeks | journal = [[American Mathematical Monthly]] | volume = 106 | pages = 393 | number = 5 | date = May 1999 | doi = 10.2307/2589143 | url = http://new.math.uiuc.edu/zipproof/zipproof.pdf | jstor = 2589143 }}; page discussing the paper: [http://new.math.uiuc.edu/zipproof/ On Conway's ZIP Proof]
*{{citation|last=Thomassen|first=Carsten|title= The Jordan-Schönflies theorem and the classification of surfaces|journal= Amer. Math. Monthly|volume= 99|issue=2|year=1992|
pages= 116–13|doi=10.2307/2324180|jstor=2324180}}, short elementary proof using spanning graphs
*{{citation|first=V.V.|last=Prasolov|title= Elements of combinatorial and differential topology|series= Graduate Studies in Mathematics|volume= 74|publisher= American Mathematical Society|year=2006|isbn= 0821838091}}, contains short account of Thomassen's proof