On linking of cycles in locally connected spaces
by
Rolando Jimenez
Instituto de Matematicas, UNAM-Mexico
Coauthors: Evgeny V. Shchepin (Steklov Institute of Mathematics, RAS-Russia)

We study linking of cycles with compacta in LCⁿ-spaces and in particular homology Z-sets. The main results are:

1. It is proved that a k-dimensional polyhedron cannot link a (n-k-1)-dimensional cycle in an n-dimensional Menger Manifolds.

2. It is proved that a compact set in an ENR is a homology Z-set provided all its points are homology Z-sets.

As a consequence of the last result we can replace ``Set'' by ``Point'' in the formulation of Edwards's FSZS Conjecture:

Given any action by a cantor group on an ENR, the free set of the action is a homology Z-set.

Date received: May 31, 2001