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The Gray filtration on phantom maps

Lê Minh Hà, Jeffrey Strom (2001)

Fundamenta Mathematicae

This paper is a study of the Gray index of phantom maps. We give a new, tower theoretic, definition of the Gray index, which allows us to study the naturality properties of the Gray index in some detail. McGibbon and Roitberg have shown that if f* is surjective on rational cohomology, then the induced map on phantom sets is also surjective. We show that if f* is surjective just in dimension k, then f induces a surjection on a certain subquotient of the phantom set. If the condition...

The Hochschild cohomology ring of the singular cochain algebra of a space

Katsuhiko Kuribayashi (2011)

Annales de l’institut Fourier

We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology is also described. In particular, when the underlying field is of characteristic two, we determine the associated bigraded Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the singular cochain on a space whose cohomology is an exterior algebra....

The homotopies of admissible multivalued mappings

Mirosław Ślosarski (2012)

Open Mathematics

Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.

The homotopy dimension of codiscrete subsets of the 2-sphere 𝕊²

J. W. Cannon, G. R. Conner (2007)

Fundamenta Mathematicae

Andreas Zastrow conjectured, and Cannon-Conner-Zastrow proved, that filling one hole in the Sierpiński curve with a disk results in a planar Peano continuum that is not homotopy equivalent to a 1-dimensional set. Zastrow's example is the motivation for this paper, where we characterize those planar Peano continua that are homotopy equivalent to 1-dimensional sets. While many planar Peano continua are not homotopy equivalent to 1-dimensional compacta, we prove that each has fundamental group that...

The homotopy groups of the L2 -localization of a certain type one finite complex at the prime 3

Yoshitaka Nakazawa, Katsumi Shimomura (1997)

Fundamenta Mathematicae

For the Brown-Peterson spectrum BP at the prime 3, v 2 denotes Hazewinkel’s second polynomial generator of B P * . Let L 2 denote the Bousfield localization functor with respect to v 2 - 1 B P . A typical example of type one finite spectra is the mod 3 Moore spectrum M. In this paper, we determine the homotopy groups π * ( L 2 M ∧ X ) for the 8 skeleton X of BP.

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