Abstract
Let Y Y be the space obtained by attaching a finite-type wedge of cells to a simply-connected, finite-type CW-complex. We introduce the free and semi-inert conditions on the attaching map which broadly generalize the previously-studied inert condition. Under these conditions we determine H ∗ ( Ω Y ; R ) H_*(\Omega Y;R) as an R R -module and as an R R -algebra, respectively. Under a further condition we show that H ∗ ( Ω Y ; R ) H_*(\Omega Y;R) is generated by Hurewicz images. As an example we study an infinite family of spaces constructed using only semi-inert cell attachments.
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