Free and semi-inert cell attachments

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 $H_{\ast }(\Omega Y;R)$ as an $R$-module and as an $R$-algebra respectively. Under a further condition we show that $H_{\ast }(\Omega Y;R)$ is generated by Hurewicz images. As an example we study an infinite family of spaces constructed using only semi-inert cell attachments.

20 pages

References in corpus (1)

• Cell attachments and the homology of loop spaces and differential graded algebras

Cited by in corpus (3)

• Separated Lie models and the homotopy Lie algebra
• The Homotopy Type of a Poincaré Duality Complex after Looping
• Graph products of spheres, associative graded algebras and Hilbert series