"Analysis Situs" is a seminal mathematics paper that Henri Poincaré published in 1895.[1] Poincaré published five supplements to the paper between 1899 and 1904.[2]
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.[3] 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
Poincaré 1895.
Poincaré 1899; Poincaré 1900; Poincaré 1902a; Poincaré 1902b; Poincaré 1904.
Dieudonné 1989: 15–35.
References
Poincaré, Henri (1895). "Analysis situs". Journal de l'École Polytechnique. (2). 1: 1–123.
Poincaré, Henri (1899). "Complément à l'Analysis Situs". Rendiconti del Circolo Matematico di Palermo. 13 (2): 285–343. doi:10.1007/BF03024461.
Poincaré, Henri (1900). "Second complément à l'Analysis Situs" (PDF). Proceedings of the London Mathematical Society. 32: 277–308. doi:10.1112/plms/s1-32.1.277.
Poincaré, Henri (1902a). "Sur certaines surfaces algébriques: troisième complément à l'Analysis Situs". Bulletin de la Société Mathématique de France. 30: 49–70. doi:10.24033/bsmf.657.
Poincaré, Henri (1902b). "Sur les cycles des surfaces algébriques: quatrième complément à l'Analysis Situs". Journal de mathématiques pures et appliquées. (5). 8: 169–214.
Poincaré, Henri (1904). "Cinquième complément à l'analysis situs". Rendiconti del Circolo Matematico di Palermo. 18: 45–110. doi:10.1007/bf03014091.
Poincaré, Henri (2009). Papers on Topology: Analysis Situs and Its Five Supplements (PDF). Translated by John Stillwell.
Dieudonné, Jean (1989). A History of Algebraic and Differential Topology 1900–1960. Boston: Birkhäuser. ISBN 0-8176-3388-X.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
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