Analysis Situs (paper)

"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]

This article is about the work by Henri Poincaré. For the book authored by Oswald Veblen, see Analysis Situs (book).

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
  1. Poincaré 1895.
  2. Poincaré 1899; Poincaré 1900; Poincaré 1902a; Poincaré 1902b; Poincaré 1904.
  3. Dieudonné 1989: 15–35.
gollark: (Works in SQLite, may work in other databases but don't count on it)
gollark: SQL!
gollark: I may be able to get it smaller, but I don't really know how.
gollark: ```sqlWITH RECURSIVE c(x)AS(VALUES(99)UNION ALL SELECT x-1 FROM c WHERE x>0),a(x, s)AS(SELECT x,SUBSTR(' bottles',1,(x<>1)+7)||' of beer'FROM c)SELECT PRINTF('%d%s on the wall%d%sTake one down, pass it around%d%s on the wall',a.x,a.s,a.x,a.s,a.x-1,b.s)FROM a JOIN a AS b ON b.x=a.x-1;```
gollark: It is done.

References


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.