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Invariants of topological spaces of dimension three play a major role in many areas, in particular . . . Introduction by the Organisers The workshop Invariants of topological spaces of dimension three, organised by Max Muster (München) and Bill E. Xample (New York) was well attended with over 30 participants with broad geographic representation from all continents. This workshop was a nice blen...

The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an a...

We establish sharp upper bounds for the topological complexity TC(X) of motion planning algorithms in topological spaces X such that the fundamental group is “small”, i.e. when π1(X) is cyclic of order ≤ 3 or has cohomological dimension ≤ 2.