Title: Free and semi-inert cell attachments
Author: Peter Bubenik
Author's e-mail address: peter.bubenik@epfl.ch
AMS classification number: 55P35 (Primary) 16E45 (Secondary)
arXive submission number: math.AT/0312387
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.