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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.

Universal acyclic resolutions for arbitrary coefficient groups

Michael Levin (2003)

Fundamenta Mathematicae

We prove that for every compactum X and every integer n ≥ 2 there are a compactum Z of dimension ≤ n+1 and a surjective U V n - 1 -map r: Z → X such that for every abelian group G and every integer k ≥ 2 such that d i m G X k n we have d i m G Z k and r is G-acyclic.

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