Free and semi-inert cell attachments
Author:
Peter Bubenik
Journal:
Trans. Amer. Math. Soc. 357 (2005), 4533-4553
MSC (2000):
Primary 55P35; Secondary 16E45
DOI:
https://doi.org/10.1090/S0002-9947-05-03989-9
Published electronically:
June 21, 2005
MathSciNet review:
2156720
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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Additional Information
Peter Bubenik
Affiliation:
Institut de Géométrie, Algèbre et Topologie, Ecole Polytechnique Fédérale de Lausanne, EPFL/SB/IGAT (BCH), 1015 Lausanne, Switzerland
ORCID:
0000-0001-5262-2133
Email:
peter.bubenik@epfl.ch
Keywords:
Cell attachments,
loop space,
loop space homology,
Adams-Hilton models,
differential graded algebras,
Lie models
Received by editor(s):
December 5, 2003
Published electronically:
June 21, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.