Equivariant strong homology (G-Ssh Homology)
by
Corina Mohorianu
Universitatea "Al. I. Cuza", Iasi, Romania

For G a compact Lie group we consider the categories G-Top, proG-Top, CPH(G-Top) and we construct the category G-Ssh.

Using the fact that every G-space X admits a G-ANR resolution (or a G-coherent expansion) first we proof that  f :X  --> Y is a G-coherent equivalence iff   f ^H: X ^H --> Y^H is an ordinary coherent equivalence for every closed subgroup H in G, where X ^H and Y^H are the corresponding inverse systems induced by X  and Y respectively. So, we have that for every F a G-Ssh morphism, F is G-Ssh equivalence iff F^H is an ordinary Ssh-equivalence for every closed subgroup H in G.

Then we define equivariant homology ^GH_n^s(X) for equivariant inverse systems X=(X_\lambda, p_\lambda^\lambda ', \Lambda ) and equivariant strong homology for G-spaces ^GH_n^s(X)=^GH_n^s(X).

Finally we proof homotopic invariance of equivariant strong homology and we deduce some long sequences for equivariant strong homology.

Date received: March 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-21.