Free and semi-inert cell attachments

Bubenik, Peter

doi:10.1090/S0002-9947-05-03989-9

Free and semi-inert cell attachments
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Trans. Amer. Math. Soc. 357 (2005), 4533-4553 Request permission

Abstract:

Let $Y$ 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 $H_*(\Omega Y;R)$ as an $R$-module and as an $R$-algebra, respectively. Under a further condition we show that $H_*(\Omega Y;R)$ 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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