Topic
Weakly contractible
About: Weakly contractible is a research topic. Over the lifetime, 20 publications have been published within this topic receiving 132 citations.
Papers
TL;DR: In this paper, a two-dimensional acyclic Eilenberg-Mac Lane space W such that, for every space X, the plus-construction X+ with respect to the largest perfect subgroup of π 1(X) coincides, up to homotopy, with the W-nullification of X; that is, the natural map X→X+ is homotopically initial among maps X→Y where the based mapping space map ∗ (W, Y) is weakly contractible.
33 citations
TL;DR: In this paper, the rational homotopy type, the minimal model and the cohomology with rational coefficients of Emb!.B 4.c/;M/ in the remaining case c 2 accrit;wM/.
Abstract: space of symplectic frames SFr.M/. We also know that the homotopy type of Emb!.B 4 .c/;M/ changes when c reaches ccrit and that it remains constant for all c2accrit;wM/. In this paper, we compute the rational homotopy type, the minimal model and the cohomology with rational coefficients of Emb!.B 4 .c/;M/ in the remaining case c2 accrit;wM/. In particular, we show that it does not have the homotopy type of a finite CW‐complex. Some of the key points in the argument are the calculation of the rational homotopy type of the classifying space of the symplectomorphism group of the blow up of M , its comparison with the group corresponding to M and the proof that the space of compatible integrable complex structures on the blow up is weakly contractible. 53D35, 57R17, 57S05; 55R20
14 citations
TL;DR: In this paper, a pointed proper model is used to classify the cofibrations that have obstruction theory with respect to all fibrations, up to weak equivalence, retract, and cobase change.
Abstract: Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial obstruction class that determines whether a lift exists. Working in an arbitrary pointed proper model category, we classify the cofibrations that have such an obstruction theory with respect to all fibrations. Up to weak equivalence, retract, and cobase change, they are the cofibrations with weakly contractible target. Equivalently, they are the retracts of principal cofibrations. Without properness, the same classification holds for cofibrations with cofibrant source. Our results dualize to give a classification of fibrations that have an obstruction theory.
13 citations
1 Jan 1996
TL;DR: The main result of as discussed by the authors is that the space of based maps from X to the profinite completion of Y is weakly contractible, which is the case for all CW-complexes.
Abstract: Let X be a connected infinite loop space whose fundamental group is a torsion group and let Y be a finite nilpotent CW-complex. The main result of this paper is that the space of based maps from X to the profinite completion of Y is weakly contractible.
8 citations
TL;DR: In this paper, it was shown that if $K$ is a nilpotent finite complex, then $Omega K$ can be built from spheres using fibrations and homotopy limits.
Abstract: We show that if $K$ is a nilpotent finite complex, then $\Omega K$ can be built from spheres using fibrations and homotopy (inverse) limits. This is applied to show that if ${\mathrm {map}}_*(X,S^n)$ is weakly contractible for all $n$, then ${\mathrm {map}}_*(X,K)$ is weakly contractible for any nilpotent finite complex $K$.
8 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2019 | 1 |
| 2016 | 1 |
| 2015 | 1 |
| 2013 | 1 |