Titlebook: A History of Algebraic and Differential Topology, 1900 - 1960; Jean Dieudonné Book 2009 Birkh?user Boston 2009 Algebraic topology.Fundamen

CRUE

CURB

Charmi Panchal,Sepinoud Azimi,Ion PetreIt took about 30 years to construct a theory of homology applicable to curvilinear “polyhedra,” embodying all the ideas of Poincaré and entirely rigorous. In a period in which the number of professional mathematicians was definitely on the increase, it is surprising that this new field of research at first attracted so few people.

博識

Agnieszka Mykowiecka,Pawel GóreckiWe have seen (chap. I, §2) that Poincaré already had a conception of .-dimensional manifolds of class C. (. integer ≥ 1 or ∞) and of analytic manifolds (sometimes called C. manifolds) which was essentially the modern one.

neutral-posture

T. M. Rezwanul Islam,Ian McQuillanI have gathered in Part 2 various results to homology which do not use homotopy theory; most of them were discovered prior to its creation. I think it is better do dissociate them form the foundational material described in Part 1, where they would have disgressed form the main themes.

Inordinate

Algorithms for Computational BiologyIn this chapter I gather miscellaneous results and techniques related to homology, in all of which the concept of . plays a more or less important part. Many of the constructions described were invented for their use in homotopy theory, leading to major results in that theory (see Part 3).

壕溝

MULKSG: ,tiple , ,imultaneous ,raph AssemblyAlgebraic geometry and algebraic topology have been linked from the beginning, since the first topological invariant, the genus of a compact Riemann surface, was introduced by Riemann in his path-breaking study of abelian integrals. His successors extended the use of similar notions to the theory of modular and automorphic functions.

perpetual