617 research outputs found
Cosimplicial resolutions and homotopy spectral sequences in model categories
We develop a general theory of cosimplicial resolutions, homotopy spectral
sequences, and completions for objects in model categories, extending work of
Bousfield-Kan and Bendersky-Thompson for ordinary spaces. This is based on a
generalized cosimplicial version of the Dwyer-Kan-Stover theory of resolution
model categories, and we are able to construct our homotopy spectral sequences
and completions using very flexible weak resolutions in the spirit of relative
homological algebra. We deduce that our completion functors have triple
structures and preserve certain fiber squares up to homotopy. We also deduce
that the Bendersky-Thompson completions over connective ring spectra are
equivalent to Bousfield-Kan completions over solid rings. The present work
allows us to show, in a subsequent paper, that the homotopy spectral sequences
over arbitrary ring spectra have well-behaved composition pairings.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper29.abs.htm
Maurer-Cartan moduli and models for function spaces
We set up a formalism of Maurer-Cartan moduli sets for L-infinity algebras
and associated twistings based on the closed model category structure on formal
differential graded algebras (a.k.a. differential graded coalgebras). Among
other things this formalism allows us to give a compact and manifestly homotopy
invariant treatment of Chevalley-Eilenberg and Harrison cohomology. We apply
the developed technology to construct rational homotopy models for function
spaces.Comment: 22 pages. This version, which will appear in Advances in Mathematics,
contains various technical corrections and updated bibliograph
On the comparison of stable and unstable P-completion
In this note we show that a p-complete nilpotent space X has a p-complete suspension spectrum if and only if its homotopy groups pi X-* are bounded p-torsion. In contrast, if pi X-* is not all bounded p-torsion, we locate uncountable rational vector spaces in the integral homology and in the stable homotopy groups of X. To prove this, we establish a homological criterion for p-completeness of connective spectra. Moreover, we illustrate our results by studying the stable homotopy groups of K(Z(p), n) via Goodwillie calculus
Pro-environmental beliefs and behaviors: two levels of response to environmental social norms
One of the ways to tackle the current environmental crisis is by trying to change beliefs and behaviors through the issuance of new laws. But laws and formal norms only become effective once they are also informally valued. This paper aims at determining whether law-regulated pro-environmental beliefs and behaviors (a) have acquired social value in Brazil, as they have in Europe and (b) pertain to two different construal levels, which could help explain the persistent belief-behavior gap in the environmental field. These two objectives are addressed in two studies using self-presentation and hetero-judgment paradigms. Results confirm the proposed hypotheses and are discussed in terms of social change for sustainability
Stratifying derived categories of cochains on certain spaces
In recent years, Benson, Iyengar and Krause have developed a theory of
stratification for compactly generated triangulated categories with an action
of a graded commutative Noetherian ring. Stratification implies a
classification of localizing and thick subcategories in terms of subsets of the
prime ideal spectrum of the given ring. In this paper two stratification
results are presented: one for the derived category of a commutative
ring-spectrum with polynomial homotopy and another for the derived category of
cochains on certain spaces. We also give the stratification of cochains on a
space a topological content.Comment: 27 page
The de Rham homotopy theory and differential graded category
This paper is a generalization of arXiv:0810.0808. We develop the de Rham
homotopy theory of not necessarily nilpotent spaces, using closed dg-categories
and equivariant dg-algebras. We see these two algebraic objects correspond in a
certain way. We prove an equivalence between the homotopy category of schematic
homotopy types and a homotopy category of closed dg-categories. We give a
description of homotopy invariants of spaces in terms of minimal models. The
minimal model in this context behaves much like the Sullivan's minimal model.
We also provide some examples. We prove an equivalence between fiberwise
rationalizations and closed dg-categories with subsidiary data.Comment: 47 pages. final version. The final publication is available at
http://www.springerlink.co
Exploring the reactivity of 2-trichloromethylbenzoxazoles for access to substituted benzoxazoles
The reactivity of 2-trichloromethylbenzoxazoles towards various nucleophiles, under metal free or iron-catalyzed conditions, for the synthesis of substituted benzoxazoles is described. These methods allow for selective substitution at either the 2- or 2’- position of the benzoxazoles using the same starting materials / reagents. This approach allows for the controlled synthesis of a variety of key derivatives from a single 2-trichloromethylbenzoxazole starting material
Brown representability for space-valued functors
In this paper we prove two theorems which resemble the classical
cohomological and homological Brown representability theorems. The main
difference is that our results classify small contravariant functors from
spaces to spaces up to weak equivalence of functors.
In more detail, we show that every small contravariant functor from spaces to
spaces which takes coproducts to products up to homotopy and takes homotopy
pushouts to homotopy pullbacks is naturally weekly equivalent to a
representable functor.
The second representability theorem states: every contravariant continuous
functor from the category of finite simplicial sets to simplicial sets taking
homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a
representable functor. This theorem may be considered as a contravariant analog
of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of
Mathematic
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