Analysis Situs (paper)
{{Short description|1895 mathematics paper by Henri Poincaré}}
{{About|the work by Henri Poincaré|the book authored by Oswald Veblen|Analysis Situs (book)}}
"Analysis Situs" is a seminal mathematics paper that Henri Poincaré published in 1895.Poincaré 1895. Poincaré published five supplements to the paper between 1899 and 1904.Poincaré 1899; Poincaré 1900; Poincaré 1902a; Poincaré 1902b; Poincaré 1904.
These papers provided the first systematic treatment of topology and revolutionized the subject by using algebraic structures to distinguish between non-homeomorphic topological spaces, founding the field of algebraic topology.Dieudonné 1989: 15–35. Poincaré's papers introduced the concepts of the fundamental group and simplicial homology, provided an early formulation of the Poincaré duality theorem, introduced the Euler–Poincaré characteristic for chain complexes, and raised several important conjectures, including the celebrated Poincaré conjecture, which was later proven as a theorem. The 1895 paper coined the mathematical term "homeomorphism".
Footnotes
References
- {{cite journal |last=Poincaré |first=Henri |author-link=Henri Poincaré |year=1895 |title=Analysis situs |journal=Journal de l'École Polytechnique |volume=1 |series=(2) |pages=1–123 |ref=Poincaré 1895 |url=http://gallica.bnf.fr/ark:/12148/bpt6k4337198/f7.image}}
- {{cite journal |last=Poincaré |first=Henri |author-link=Henri Poincaré |year=1899 |title=Complément à l'Analysis Situs |journal=Rendiconti del Circolo Matematico di Palermo |volume=13 |issue= 2|pages=285–343 |url=https://zenodo.org/record/2063679|doi=10.1007/BF03024461 }}
- {{cite journal |last=Poincaré |first=Henri |author-link=Henri Poincaré |year=1900 |title=Second complément à l'Analysis Situs |journal=Proceedings of the London Mathematical Society |volume=32 |pages=277–308 |doi=10.1112/plms/s1-32.1.277|url=https://zenodo.org/record/1447744/files/article.pdf }}
- {{cite journal |last=Poincaré |first=Henri |author-link=Henri Poincaré |year=1902a |title=Sur certaines surfaces algébriques: troisième complément à l'Analysis Situs |journal=Bulletin de la Société Mathématique de France |volume=30 |pages=49–70 |url=http://www.numdam.org/numdam-bin/feuilleter?id=BSMF_1902__30_|doi=10.24033/bsmf.657 |doi-access=free }}
- {{cite journal |last=Poincaré |first=Henri |author-link=Henri Poincaré |year=1902b |title=Sur les cycles des surfaces algébriques: quatrième complément à l'Analysis Situs |journal=Journal de mathématiques pures et appliquées |volume=8 |series=(5) |pages=169–214 |url=http://gallica.bnf.fr/ark:/12148/bpt6k1074672/f170.image.r=Journal%20mathématiques%20pures%20appliquées.langFR}}
- {{cite journal |last=Poincaré |first=Henri |author-link=Henri Poincaré |year=1904 |title=Cinquième complément à l'analysis situs |journal=Rendiconti del Circolo Matematico di Palermo |volume=18 |pages=45–110 |url= https://zenodo.org/record/1428448|doi=10.1007/bf03014091}}
- {{cite book
|last=Poincaré |first=Henri|author-link=Henri Poincaré
|title=Papers on Topology: Analysis Situs and Its Five Supplements
|year=2009
|translator=John Stillwell
|translator-link=John Stillwell
|url=http://www.maths.ed.ac.uk/~aar/papers/poincare2009.pdf}}
- {{cite book | last = Dieudonné | first = Jean | author-link = Jean Dieudonné | title = A History of Algebraic and Differential Topology 1900–1960 | publisher = Birkhäuser | location = Boston | year = 1989 | isbn = 0-8176-3388-X | url-access = registration | url = https://archive.org/details/historyofalgebra0000dieu_g9a3 }}
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