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.
• Dieudonné, Jean A History of Algebraic and Differential Topology 1900-1960. Boston: Birkhäuser.