Fibrations and homotopy type
نویسندگان
چکیده
منابع مشابه
Fibrations and Homotopy Colimits of Simplicial Sheaves
We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors between categories of simplicial sheaves preserve homotopy pullback squares. The method we use introduces the notion of a sharp map, which is analogous to the no...
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In [HS] and [F1] Halperin, Stasheff, and Félix showed how an inductively-defined sequence of elements in the cohomology of a graded commutative algebra over the rationals can be used to distinguish among the homotopy types of all possible realizations, thus providing a collection of algebraic invariants for distinguishing among rational homotopy types of spaces. There is also a dual version, in...
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Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.
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The purpose of this informal survey article is to introduce the reader to a new and surprising connection between Geometry, Algebra, and Logic, which has recently come to light in the form of an interpretation of the constructive type theory of Per Martin-Löf into homotopy theory, resulting in new examples of certain algebraic structures which are important in topology. This connection was disc...
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Take M , a finite-dimensional differentiable manifold, and f : M → R a smooth function. Such a function f is called a Morse function if it has no degenerate critical points. Morse theory allows us to connect the topology, in particular the homotopy type, of M with the behavior of f on M . In the following sections, we will state and prove two important theorems in Morse theory. Using these two ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1984
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1984-0733417-7