喧闹
发表于 2025-3-23 13:01:50
Introduction: Where Are We Now?ns of homotopy theory: extension and lifting problems. The notion of hom-otopy is introduced, and its connection with the above problems discussed. This leads to a formulation of fibrations and cofibrations, which have played such a fundamental role in the development of the subject.
钳子
发表于 2025-3-23 14:24:16
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头脑冷静
发表于 2025-3-23 18:30:46
The Future Nature of Consulting Servicesory . to the category of groups if . = 1, abelian groups if . 1. In certain respects, they resemble the homology groups, and one of the objectives of this chapter is to pursue this analogy and see where it may lead.
拉开这车床
发表于 2025-3-24 01:46:59
Anthony J. Berry,Jane Broadbent,David Otleyr all .. The next step is the determination of . .. By the results of §2 of Chapter II, . is a free abelian group with one basis element for each .-cell of .. We have seen that the Hurewicz map .: . . → . is an epimorphism whose kernel is generated by all elements of the form . — . (.) with α . . .
Brain-Waves
发表于 2025-3-24 05:05:39
Jane Broadbent,Richard Laughline of the last chapter. If . → . is a cross-section over the .-skeleton, the problem of extending . reduces to a family of local problems: for each . + l)-cell . of ., the induced fibration over Δ. is fibre homotopically trivial. Its total space may thus be represented as a product Δ. x ., where . is
Carminative
发表于 2025-3-24 09:36:02
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窃喜
发表于 2025-3-24 14:14:29
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synovium
发表于 2025-3-24 16:24:12
David Ashton,Mark Easterby-Smiths group need not be abelian (although it is if . is the suspension of a space .). It is natural to ask whether it may be nilpotent. It turns out that the degree of nilpotence is closely related to the Lusternik-Schnirelmann category of the space . Indeed, a mild change in the definition of the latte
Antarctic
发表于 2025-3-24 21:32:24
https://doi.org/10.1007/978-3-319-40778-4s. The universal example for operations in one variable is a sphere; for operations in several variables it is a cluster . of spheres. More precisely, let a e α ∈ . (∑), and let . ∈ . . 1,…, .. Then there is a map . : ∑ → X such that .| S. represents ., and the correspondence. is a homotopy operatio
Precursor
发表于 2025-3-25 02:30:13
Law and Business: Comparative Perspectivesd pair .. The homology groups of the triples (., X., .) are linked together in an intricate way. They can, however, be assembled into two graded groups which are connected by an exact triangle. Such a diagram is called an exact couple; the notion is due to Massey . The basic operation on exact