Fibrewise localization and completion

Fibrewise Localization and Completion

The behavior of fibrewise localization and completion on the classifying space level is analyzed. The relationship of these constructions to fibrewise joins and smash products and to orientations of spherical fibrations is also analyzed. This theory is essential to validate Sullivan's proof of the Adams conjecture. In Sullivan's beautiful proof of the Adams conjecture [20], perhaps the crucial ...

Amodal completion and localization

In a three-line vernier acuity task, a central line was localized between two aligned line segments. Accuracy did not improve when the segments formed a unified amodally completed percept. In a two-line vernier acuity task, a line was localized below a target line placed next to a physically segmented flank stimulus. Shifts in mean points of subjective equality suggested that amodally completed...

Poincaré Duality Embeddings and Fibrewise

We prove a relative Poincaré embedding theorem for maps of pairs into a Poincaré pair. This result has applications: it is the engine of the compression theorem of the author’s paper in Algebr. Geom. Topol. 2, (2002) 311–336, it yields a Poincaré space version of Hudson’s embedding theorem, and it can be used to equip 2-connected Poincaré spaces with handle decompositions.

Localization and Completion in Homotopy Theory

Fibrewise injectivity and Kock-Zöberlein monads

Using Escardó-Flagg approach to injectivity via Kock-Zöberlein monads in T0 topological spaces [3], and Hofmann’s recent study of injectivity for spaces [4], we characterize continuous maps which are injective with respect to special classes of embeddings using convergence: see [1]. In fact, convergence has been shown to be very useful in the characterization of special classes of maps, like ef...