A new geometric invariant associated to the space of flat connections
We construct a locally compact 2-dimensional polyhedron X which does not admit a 𝒵-compactification, but which becomes 𝒵-compactifiable upon crossing with the Hilbert cube. This answers a long-standing question posed by Chapman and Siebenmann in 1976 and repeated in the 1976, 1979 and 1990 versions of Open Problems in Infinite-Dimensional Topology. Our solution corrects an error in the 1990 problem list.
Arhangel’skiǐ proved that if and are completely regular spaces such that and are linearly homeomorphic, then is pseudocompact if and only if is pseudocompact. In addition he proved the same result for compactness, -compactness and realcompactness. In this paper we prove that if is a continuous linear surjection, then is pseudocompact provided is and if is a continuous linear injection, then is pseudocompact provided is. We also give examples that both statements do not hold...
We compute the height of the third Stiefel--Whitney characteristic class of the canonical bundles over some infinite classes of Grassmann manifolds of five dimensional vector subspaces of real vector spaces.
The Polish space Y constructed in [vM1] admits no nontrivial isotopy. Yet, there exists a Polish group that acts transitively on Y.