Contractibility of Whitney continua in C(X)

A note on a Whitney map for continua

Let X be a non-metric continuum, and C(X) the hyperspace of subcontinua of X. It is known that there is no Whitney map on the hyperspace 2 for non-metrizable Hausdorff compact spaces X. On the other hand, there exist non-metrizable continua which admit and the ones which do not admit a Whitney map for C(X). In this paper we investigate the properties of non-metrizable continua which admit a Whi...

A1-contractibility and topological contractibility

These notes are an extended transcript of two lectures given at the University of Ottawa during the workshop “Group actions, generalized cohomology theories, and affine algebraic geometry." The first lecture was a general introduction to A1-homotopy theory focusing on motivating the choice of definitions in the construction, together with a definition of A1-contractible spaces. The second lectu...

The Planarity Theorems of MacLane and Whitney for Graph-like Continua

The planarity theorems of MacLane and Whitney are extended to compact graph-like spaces. This generalizes recent results of Bruhn and Stein (MacLane’s Theorem for the Freudenthal compactification of a locally finite graph) and of Bruhn and Diestel (Whitney’s Theorem for an identification space obtained from a graph in which no two vertices are joined by infinitely many edge-disjoint paths).

Topology Proceedings 1 (1976) pp. 209-219: SOME PROPERTIES OF WHITNEY CONTINUA IN THE HYPERSPACE C(X)

Contractibility and NP-completeness

For a fixed graph H, let H-CON denote the problem of determining whether a given graph is contractible to H. The complexity of H-CON is studied for H belonging to certain classes of graphs, together covering all connected graphs of order at most 4. In particular, H-CON is NP-complete if H is a connected triangle-free graph other than a star. For each connected graph H of order a t most 4 other ...