Interactions between Homotopy and Topological Groups in Covering (C, R) Space Embeddings

Local Homotopy Properties of Topological Embeddings in Codimension Two

A b str act . Suppose N is an (n− 2)-manifold topologically embedded in an n-manifold M . Chapman and Quinn have shown that N is locally flat in M provided that the local homotopy groups of M − N at points of N are infinite cyclic and that all the higher local homotopy groups of M−N at points of N vanish. The main theorem in this paper asserts that it is only necessary to assume the homotopy co...

Covering Groups of Non-connected Topological Groups Revisited

All spaces are assumed to be locally path connected and semi-locally 1-connected. Let X be a connected topological group with identity e, and let p : X̃ → X be the universal cover of the underlying space of X. It follows easily from classical properties of lifting maps to covering spaces that for any point ẽ in X̃ with pẽ = e there is a unique structure of topological group on X̃ such that ẽ is th...

The Covering Homotopy Extension Problem for Compact Transformation Groups

It is shown that the orbit space of universal (in the sense of Palais) G-spaces classifies G-spaces. Theorems on the extension of covering homotopy for G-spaces and on a homotopy representation of the isovariant category ISOV are proved . DOI: 10.1134/S0001434612110016

The Group of Homotopy Equivalences of a Space by M. Arkowitz and C. R. Curjel

Generalized Covering Groups and Direct Limits