Higher topological complexity of aspherical spaces

New Lower Bounds for the Topological Complexity of Aspherical Spaces

We show that the topological complexity of an aspherical space X is bounded below by the cohomological dimension of the direct product A×B, whenever A and B are subgroups of π1(X) whose conjugates intersect trivially. For instance, this assumption is satisfied whenever A and B are complementary subgroups of π1(X). This gives computable lower bounds for the topological complexity of many groups ...

Topological spaces associated to higher-rank graphs

We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that identifying isomorphic co-hereditary subgraphs in a disjoint union of two rank-k graphs gives rise to pullbacks of the associated C∗algebras. We describe a combinat...

REDUNDANCY OF MULTISET TOPOLOGICAL SPACES

In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.

Topological rigidity for non-aspherical manifolds by

The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f : N → M is an orientation preserving homotopy equivalence with a closed oriented manifold as target, then there is an orientation preserving homeomorphism h : N → M such that h an...

σ-Normality of Topological Spaces