"Analysis Situs" is a seminal
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
paper that
Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
published in 1895. Poincaré published five supplements to the paper between 1899 and 1904.
These papers provided the first systematic treatment of
topology and revolutionized the subject by using algebraic structures to distinguish between non-
homeomorphic
In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphi ...
topological spaces, founding the field of
algebraic topology.
[Dieudonné 1989: 15–35.] Poincaré's papers introduced the concepts of the
fundamental group
In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of ...
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
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Mathematics papers
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