共查询到20条相似文献,搜索用时 46 毫秒
1.
Julia E. Bergner 《Topology》2007,46(4):397-436
Given any model category, or more generally any category with weak equivalences, its simplicial localization is a simplicial category which can rightfully be called the “homotopy theory” of the model category. There is a model category structure on the category of simplicial categories, so taking its simplicial localization yields a “homotopy theory of homotopy theories”. In this paper we show that there are two different categories of diagrams of simplicial sets, each equipped with an appropriate definition of weak equivalence, such that the resulting homotopy theories are each equivalent to the homotopy theory arising from the model category structure on simplicial categories. Thus, any of these three categories with the respective weak equivalences could be considered a model for the homotopy theory of homotopy theories. One of them in particular, Rezk’s complete Segal space model category structure on the category of simplicial spaces, is much more convenient from the perspective of making calculations and therefore obtaining information about a given homotopy theory. 相似文献
2.
Matias L. del Hoyo 《Topology and its Applications》2008,155(11):1189-1200
We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of spaces and small categories, by using partially ordered sets. This yields a new conceptual proof to the well-known fact that these two homotopy categories are equivalent. 相似文献
3.
The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact
spaces and manifolds. The notion of exterior weak ℕ-S-equivalences is given by exterior maps which induce isomorphisms on the k-th ℕ-exterior homotopy groups for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray localized by exterior weak ℕ-S-equivalences is called the category of exterior ℕ-S-types. The existence of closed model structures in the category of exterior spaces permits to establish equivalences between
homotopy categories obtained by dividing by exterior homotopy relations, and categories of fractions (localized categories)
given by the inversion of classes of week equivalences. The family of neighbourhoods ‘at infinity’ of an exterior space can
be interpreted as a global prospace and under the condition of first countable at infinity we can consider a global tower
instead of a prospace. The objective of this paper is to use localized categories to find the connection between S-types of exterior spaces and S-types of global towers of spaces. The main result of this paper establishes an equivalence between the category of S-types of rayed first countable exterior spaces and the category of S-types of global towers of pointed spaces. As a consequence of this result, categories of global towers of algebraic models
localized up to weak equivalences can be used to give some algebraic models of S-types.
The authors acknowledge the financial support given by the projects FOMENTA 2007/03 and MTM2007-65431. 相似文献
4.
王玉玉 《数学年刊A辑(中文版)》2018,39(3):273-286
本文中,通过几何方法证明了σ相关同伦元素在球面稳定同伦群π_mS中是非平凡的,其中m=p~(n+1)q+2p~nq+(s+3)p~2q+(s+3)pq+(s+3)q-8,p≥7是奇素数,n3,0≤sp-3,且q=2(p-1).该σ相关同伦元素在Adams谱序列的E_2-项中由■_s+3■_ng0表示. 相似文献
5.
Marcin Sawicki 《Topology and its Applications》2005,150(1-3):59-78
This paper deals with extending maps in asymptotic categories, i.e., in categories consisting of metric spaces and asymptotically Lipschitz coarsely proper maps. We demonstrate certain examples of absolute extensors and absolute neighborhood extensors. We give some conditions under which a version of Borsuk's homotopy extension theorem holds in these categories, and in answer to a problem posed by Dranishnikov in [Russian Math. Surveys 55 (2000) 1085] we show the failure of a general homotopy extension theorem. Finally, we show that a pair of an Hadamard space and its convex subspace has the homotopy extension property. 相似文献
6.
Youhua Qian & Shengmin Chen 《数学研究通讯:英文版》2009,25(2):97-103
Let Aut$_∗(X)$ denote the group of homotopy classes of self-homotopy
equivalences of $X$, which induce identity automorphisms of homology group. We
describe a decomposition of Aut$_∗(X_1∨· · ·∨X_n)$ as a product of its simpler subgroups.
We consider the subgroup Aut$_Σ(X)$ of all self homotopy classes α of $X$ such that $Σα = 1_{ΣX} : ΣX → ΣX$, and also give some properties of Aut$_Σ(X)$. 相似文献
7.
Gonçalo Tabuada 《Topology and its Applications》2010,157(3):563-593
We establish a connection between differential graded and simplicial categories by constructing a three-step zig-zag of Quillen adjunctions relating the homotopy theories of the two. In an intermediate step, we extend the Dold-Kan correspondence to a Quillen equivalence between categories enriched over non-negatively graded complexes and categories enriched over simplicial modules. As an application, we obtain a simple calculation of Simpson's homotopy fiber, which is known to be a key step in the construction of a moduli stack of perfect complexes on a smooth projective variety. 相似文献
8.
设$p\geq 7$素数,$A$为模$p$的Steenrod代数. 我们利用Adams谱序列证明了球面稳定同伦群$\pi_{\ast}S$中,存在由$b_1g_0\tilde{\gamma}_{s}\in Ext_A^{s+4,(s+1)p^2q+spq+sq+s-3}(Z_p,Z_p)$所表示的新的非平凡元素族,其中$q=2(p-1)$, $3\leq s
相似文献
9.
Julia E. Bergner 《Israel Journal of Mathematics》2011,185(1):389-411
Given an appropriate diagram of left Quillen functors between model categories, one can define a notion of homotopy fiber
product, but one might ask if it is really the correct one. Here, we show that this homotopy pullback is well-behaved with
respect to translating it into the setting of more general homotopy theories, given by complete Segal spaces, where we have
well-defined homotopy pullbacks. 相似文献
10.
Let X be a topological space.In this survey the authors consider several types of configuration spaces,namely,the classical(usual)configuration spaces F_n(X)and D_n(X),the orbit configuration spaces F_n~G(X)and F_n~G(X)/S_nwith respect to a free action of a group G on X,and the graph configuration spaces F_n~Γ(X)and F_n~Γ(X)/H,whereΓis a graph and H is a suitable subgroup of the symmetric group S_n.The ordered configuration spaces F_n(X),F_n~G(X),F_n~Γ(X)are all subsets of the n-fold Cartesian product ∏_1~nX of X with itself,and satisfy F_n~G(X)?F_n(X)?F_n~Γ(X)?∏_1~nX.If A denotes one of these configuration spaces,the authors analyse the difference between A and ∏_1~nXfrom a topological and homotopical point of view.The principal results known in the literature concern the usual configuration spaces.The authors are particularly interested in the homomorphism on the level of the homotopy groups of the spaces induced by the inclusionι:A-→∏_1~nX,the homotopy type of the homotopy fibre I_ιof the mapιvia certain constructions on various spaces that depend on X,and the long exact sequence in homotopy of the fibration involving I_ιand arising from the inclusionι.In this respect,if X is either a surface without boundary,in particular if X is the 2-sphere or the real projective plane,or a space whose universal covering is contractible,or an orbit space S~k/Gof the k-dimensional sphere by a free action of a Lie group G,the authors present recent results obtained by themselves for the first case,and in collaboration with Golasi′nski for the second and third cases.The authors also briefly indicate some older results relative to the homotopy of these spaces that are related to the problems of interest.In order to motivate various questions,for the remaining types of configuration spaces,a few of their basic properties are described and proved.A list of open questions and problems is given at the end of the paper. 相似文献
11.
Shu-Gong Zhang & Guo-Chen Feng 《计算数学(英文版)》1992,10(3):263-272
To solve $F(x)=0$ numerically, we first prove that there exists a tube-like neighborhood around the curve in $R^n$ defined by the Newton homotopy in which $F(x)$ possesses some good properties. Then in this neighborhood, we set up an algorithm which is numerically stable and convergent. Since we can ensure that the iterative points are not far from the homotopy curve while computing, we need not apply the predictor-corrector which is often used in path following methods. 相似文献
12.
Dae-Woong LEE 《数学年刊B辑(英文版)》2016,37(6):951-962
Given a connected CW-space X, SN T(X) denotes the set of all homotopy types[X′] such that the Postnikov approximations X~((n)) and X′~((n)) are homotopy equivalent for all n. The main purpose of this paper is to show that the set of all the same homotopy ntypes of the suspension of the wedges of the Eilenberg-MacL ane spaces is the one element set consisting of a single homotopy type of itself, i.e., SNT(Σ(K(Z, 2a_1) ∨ K(Z, 2a_2) ∨···∨ K(Z, 2a_k))) = * for a_1 a_2 ··· a_k, as a far more general conjecture than the original one of the same n-type posed by McG ibbon and M?ller(in [McG ibbon, C. A. and M?ller, J. M., On infinite dimensional spaces that are rationally equivalent to a bouquet of spheres, Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Lecture Notes in Math., 1509, 1992, 285–293].) 相似文献
13.
Fabian Lenhardt 《Journal of Pure and Applied Algebra》2012,216(5):1080-1091
14.
Dan Kucerovsky 《Proceedings of the American Mathematical Society》2007,135(2):405-415
Fredholm triples are used in the study of Kasparov's -groups, and in Connes's noncommutative geometry. We define an absorption property for Fredholm triples, and give an if and only if condition for a Fredholm triple to be absorbing. We study the interaction of the absorption property with several of the more common equivalence relations for Fredholm triples. In general these relations are coarser than homotopy in the norm topology. We give simple conditions for an equivalence of triples to be implemented by an operator homotopy (i.e. a homotopy with respect to the norm topology). This can be expected to have applications in index theory, as we illustrate by proving two theorems of Pimsner-Popa-Voiculescu type. We show that there is some relationship with the interesting Toms-Winter characterization of -absorbing algebras, recently obtained as part of Elliott's classification program.
15.
Kathryn Hess 《Applied Categorical Structures》2002,10(3):195-220
This survey of model categories and their applications in algebraic topology is intended as an introduction for non homotopy theorists, in particular category theorists and categorical topologists. We begin by defining model categories and the homotopy-like equivalence relation on their morphisms. We then explore the question of compatibility between monoidal and model structures on a category. We conclude with a presentation of the Sullivan minimal model of rational homotopy theory, including its application to the study of Lusternik–Schnirelmann category. 相似文献
16.
Hans-joachim Baues 《K-Theory》1999,17(2):151-193
The homotopy category of one point unions of spheres and the homotopy category of Eilenberg–MacLane spaces are examples of graded theories. Spaces yield models of these theories which can be described in terms of iterated comma categories given by functors. The associated derived functors play an important role in spectral sequences computing homotopy groups. Using cross-effect methods, the derived functors are studied and the existence of a vanishing line is proven. 相似文献
17.
This is the third paper in a series. In Part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and derived categories of abelian categories. Then we consider examples from (noncommutative) algebraic geometry. In particular, we study noncommutative Grassmanians that are true noncommutative moduli spaces of structure sheaves of projective subspaces in projective spaces. 相似文献
18.
设 $p\geq 7$ 为任意奇素数. 证明了当 $3\leq s
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19.
Classical homological algebra takes place in additive categories. In homotopy theory such additive categories arise as homotopy categories of “additive groupoid enriched categories”, in which a secondary analog of homological algebra can be performed. We introduce secondary chain complexes and secondary resolutions leading to the concept of secondary derived functors. As a main result we show that the E3-term of the Adams spectral sequence can be expressed as a secondary derived functor. This result can be used to compute the E3-term explicitly by an algorithm. 相似文献
20.
Stability analysis and approximate solution of SIR epidemic model with Crowley-Martin type functional response and Holling type-II treatment rate by using homotopy analysis method 下载免费PDF全文
Parvaiz Ahmad Naik Jian Zu Mohammad Ghoreishi 《Journal of Applied Analysis & Computation》2020,10(4):1482-1515
In this paper, SIR epidemic model with Crowley-Martin type functional response and Holling type-II treatment rate is investigated. The analysis of the model shows that it has two equilibria, namely disease-free and endemic. We investigate the existence and stability results of equilibria by using LaSalle''s invariant principle and Lyapunov function. $\mathfrak{R}_{0}$ has been found to ensure the extinction or persistence of the infection. Furthermore, homotopy analysis method is employed to obtain the series solution of the proposed model. By using the homotopy solutions, firstly, several $\hbar$-curves are plotted to demonstrate the regions of convergence, then the residual and square residual errors are obtained for different values of these regions. Secondly, the numerical solutions are presented for various iterations and the absolute error functions are applied to show the accuracy of the applied homotopy analysis method. 相似文献