| 1. |
- Chachólski, Wojciech, et al.
(författare)
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Cellular covers of divisible abelian groups
- 2009
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Ingår i: ALPINE PERSPECTIVES ON ALGEBRAIC TOPOLOGY. - 9780821848395 ; , s. 77-97
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Konferensbidrag (refereegranskat)abstract
- We determine all the possible values of the cellular approximation functor c(A) : cell(A)E -> E, where A is an arbitrary group and E is a divisible abelian group.
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| 2. |
- Chacholski, Wojciech, et al.
(författare)
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Homotopy Exponents for Large H-Spaces
- 2008
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Ingår i: International mathematics research notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247.
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Tidskriftsartikel (refereegranskat)abstract
- We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.
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| 3. |
- Chacholski, Wojciech, et al.
(författare)
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Homotopy pull-back squares up to localization
- 2006
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Ingår i: Alpine Anthology of Homotopy Theory. - PROVIDENCE : AMER MATHEMATICAL SOC. - 082183696X ; , s. 55-72
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Konferensbidrag (refereegranskat)abstract
- We characterize the class of homotopy pull-back squares by means of elementary closure properties. The so called Puppe theorem which identifies the homotopy fiber of certain maps constructed as homotopy colimits is a straightforward consequence. Likewise we characterize the class of squares which are homotopy pull-backs "up to Bousfield localization". This yields a generalization of Puppe's theorem which allows us to identify the homotopy type of the localized homotopy fiber. When the localization functor is homological localization this is one of the key ingredients in the group completion theorem.
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| 4. |
- Chacholski, Wojciech, et al.
(författare)
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nu(*)-torsion spaces and thick classes
- 2006
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 336:1, s. 13-26
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Chacholski, Wojciech, et al.
(författare)
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Representations of spaces
- 2008
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Ingår i: Algebraic and Geometric Topology. - : Mathematical Sciences Publishers. - 1472-2747 .- 1472-2739. ; 8:1, s. 245-278
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Tidskriftsartikel (refereegranskat)abstract
- We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces to be able to construct resolutions. We prove that the homotopy category of any monoidal model category is always a central algebra over the homotopy category of Spaces.
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| 6. |
- Chacholski, Wojciech, et al.
(författare)
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The A-core and A-cover of a group
- 2009
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Ingår i: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 321:2, s. 631-666
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Tidskriftsartikel (refereegranskat)abstract
- This paper provides a comprehensive investigation of the cellular approximation functor cell(A) G, in the category of groups. approximating a group G by a group A. We also study related notions such as A-injection, A-generation and A-constructibility of a group G and we find several interesting connections with the Schur multiplier H-2(G, Z). Our constructions are direct and are given in a slow and detailed manner.
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| 7. |
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| 8. |
- Nordström, Fredrik, 1978-
(författare)
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Cofinality Properties of Categories of Chain Complexes
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis treats a family of categories, the chain categories of an A-module M, and functors indexed by them. Among the chain categories are two classical constructions; the category of finitely generated projective Amodules, and the category of finitely generated free A-modules, here denoted by P0(0) and Sing(0) respectively. The focus of this thesis is on how to construct homotopy colimits of functors indexed by chain categories, and taking values in non-negative chain complexes of A-modules. One consequence of Lazard’s theorem is that if M is flat, then all functors over Sing(M) are flat; that is, the homotopy colimits of these functors are weakly equivalent to the ordinairy colimits. A motivating question has been to understand when functors over Sing(M) are flat for non-flat M. In particular, when the forgetful functor UM is flat. One of the results obtain is that if A is Noetherian, then UM is flat over many chain categories, and this property is independent of M. In contrast, if A is commutative, then the pointwise tensor product UM UM is defined, and this is not a flat functor in general, even if UM is flat. The key notion used to study these questions is that of a cofinal functor. Among the main results are the cofinality of various inclusion functors among the chain categories themselves, and the existence, construction and classification of cofinal simplicial objects in P0(M) and Sing(M). Also, a method to construct flat resolutions of functors indexed by P0 and taking values in A-modules is developed (but applicability of this construction depends on severe restrictions on M). These methods are used to compute the homotopy colimits of several functors defined over various chain categories.
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