We provide a tool for studying properly discontinuous actions of non-compact groups on locally compact, connected and paracompact spaces, by embedding such an action in a suitable zero-dimensional compactification of the underlying space with pleasant properties. Precisely, given such an action (G,X) we construct a zero-dimensional compactification μX of X with the properties: (a) there exists ...

The anisotropic blowup along the zero section and the fiberwise compactification of a real vector bundle F → X are manifolds with boundary for which the natural structure bundle is the b-tangent bundle. We give a necessary and sufficient condition for these procedures to give a b-complex structure when applied to a holomorphic vector bundle over a complex manifold, and analyze some aspects of t...

‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...

Abstract We identify the exit path $\infty $-category of reductive Borel–Serre compactification as nerve a $1$-category defined purely in terms rational parabolic subgroups and their unipotent radicals. As immediate consequences, we fundamental group compactification, recovering result Ji–Murty–Saper–Scherk, obtain combinatorial incarnation constructible complexes sheaves on elements derived fu...