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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite $ {\mathbb{Z}}/2{\mathbb{Z}}$-CW complexes which are not homotopically stratified by orbit type


Authors: Andrew Nicas and David Rosenthal
Journal: Proc. Amer. Math. Soc. 137 (2009), 381-384
MSC (2000): Primary 57N80, 57S17, 57N40
Published electronically: August 1, 2008
MathSciNet review: 2439463
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Abstract: For $ k \geq 2$, we construct finite $ {\mathbb{Z}}/2{\mathbb{Z}}$-CW complexes with one $ {\mathbb{Z}}/2{\mathbb{Z}}$-cell in dimensions 0, $ 1$ and $ k+1$. Using a theorem of Bruce Hughes, we show that these complexes are not homotopically stratified by orbit type in the sense of Quinn.


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Additional Information

Andrew Nicas
Affiliation: Department of Mathematics & Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
Email: nicas@mcmaster.ca

David Rosenthal
Affiliation: Department of Mathematics and Computer Science, St. Johns University, 8000 Utopia Parkway, Jamaica, New York 11439
Email: rosenthd@stjohns.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09647-0
PII: S 0002-9939(08)09647-0
Keywords: CW complex, homotopically stratified, orbit type
Received by editor(s): December 14, 2007
Published electronically: August 1, 2008
Additional Notes: The first author was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2008 American Mathematical Society