Analysis Situs (book)

Analysis Situs (book)

Analysis Situs is an influential mathematical paper (and a series of addenda) written by Henri Poincaré. Besides providing the first systematic treatment of topology, Poincaré revolutionized the subject by using algebraic structures to distinguish between non-homeomorphic topological spaces, effectively creating the subject of algebraic topology.

In the papers he introduced the concepts of fundamental group and simplicial homology, provided an early formulation of Poincaré duality, gave the Euler-Poincaré characteristic for chain complexes, and mentioned several important conjectures including the Poincaré conjecture..

References

* Henri Poincaré, "Analysis Situs", Journal de l'École Polytechnique ser 2, 1 (1895) pages 1-123.
* Henri Poincaré, "Complément à l'Analysis Situs", Rendiconti del Circolo matematico di Palermo, 13 (1899) pages 285-343.
* Henri Poincaré, "Second complément à l'Analysis Situs", Proceedings of the London Mathematical Society, 32 (1900), pages 277-308.
* Henri Poincaré, "Sur certaines surfaces algébriques ; troisième complément à l'Analysis Situs", Bulletin de la Société mathématique de France, 30 (1902), pages 49-70.
* Henri Poincaré, "Sur les cycles des surfaces algébriques ; quatrième complément à l'Analysis Situs", Journal de mathématiques pures et appliquées, 5° série, 8 (1902), pages 169-214.
* Henri Poincaré, "Cinquième complément à l'analysis situs", Rendiconti del Circolo matematico di Palermo 18 (1904) pages 45-110.
*


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Analysis situs — may refer to: * Analysis Situs (book), a work on topology by Henri Poincaré *Analysis situs, an obsolete synonym for topology …   Wikipedia

  • List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …   Wikipedia

  • List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia

  • Gottfried Leibniz — Infobox Philosopher region = Western Philosophy era = 18th century philosophy color = #B0C4DE |250px image caption = Gottfried Wilhelm Leibniz name = Gottfried Wilhelm Leibniz birth = 1 July (21 June Old Style) 1646, Leipzig, Electorate of Saxony …   Wikipedia

  • topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c …   Universalium

  • History of geometry — Geometry (Greek γεωμετρία ; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre modern mathematics, the other being the study of numbers. Classic geometry… …   Wikipedia

  • Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… …   Wikipedia

  • Situationist International — The Situationist International (SI) was a small group of international political and artistic agitators with roots in Marxism, Lettrism and the early 20th century European artistic and political avant gardes. Formed in 1957, the SI was active in… …   Wikipedia

  • Early Islamic philosophy — or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar (early 9th century CE) and lasting until the 6th century AH (late 12th century CE). The period is known as… …   Wikipedia

  • Charles Sanders Peirce —  B …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”