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There Are No Essential Phantom Mappings from 1-dimensional CW-complexes

Sibe Mardešić (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

A phantom mapping h from a space Z to a space Y is a mapping whose restrictions to compact subsets are homotopic to constant mappings. If the mapping h is not homotopic to a constant mapping, one speaks of an essential phantom mapping. The definition of (essential) phantom pairs of mappings is analogous. In the study of phantom mappings (phantom pairs of mappings), of primary interest is the case when Z and Y are CW-complexes. In a previous paper it was shown that there are no essential phantom...

Topological complexity of motion planning and Massey products

Mark Grant (2009)

Banach Center Publications

We employ Massey products to find sharper lower bounds for the Schwarz genus of a fibration than those previously known. In particular we give examples of non-formal spaces X for which the topological complexity TC(X) (defined to be the genus of the free path fibration on X) is greater than the zero-divisors cup-length plus one.

Transfert algébrique et action du groupe linéaire sur les puissances divisées modulo 2

Tran Ngoc Nam (2008)

Annales de l’institut Fourier

On détermine la dimension d’une représentation du groupe linéaire définie par un sous-espace vectoriel de l’algèbre à puissances divisées, puis on explicite l’image du transfert algébrique en degré générique et celle du transfert algébrique quadruple, et finalement on identifie les indécomposables de degré pair de l’algèbre polynomiale à quatre variables, vue comme module sur l’algèbre de Steenrod.

Truncated polynomial algebras over the Steenrod algebra.

Mohamed Ali (1990)

Publicacions Matemàtiques

It is shown that the classification of polynomial algebras over the mod p Steenrod algebra is an essentially different problem from the classification of polynomial algebras truncated at height greater than p over the Steenrod algebra.

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