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The loop group and the cobar construction
Author(s):
Kathryn
Hess;
Andrew
Tonks
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1861-1876.
MSC (2010):
Primary 55P35;
Secondary 16T05, 18G30, 55U10, 57T05, 57T30
Posted:
December 21, 2009
MathSciNet review:
2587471
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Abstract:
We prove that for any  -reduced simplicial set  , Adams' cobar construction  on the normalised chain complex of  is naturally a strong deformation retract of the normalised chains  on the Kan loop group  . In order to prove this result, we extend the definition of the cobar construction and actually obtain the existence of such a strong deformation retract for all 0-reduced simplicial sets.
References:
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Additional Information:
Kathryn
Hess
Affiliation:
Institut de géométrie, algèbre et topologie (IGAT), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Email:
kathryn.hess@epfl.ch
Andrew
Tonks
Affiliation:
Statistics, OR and Mathematics Research Centre (STORM), London Metropolitan University, 166-220 Holloway Road, London N7 8DB, United Kingdom
Email:
a.tonks@londonmet.ac.uk
DOI:
10.1090/S0002-9939-09-10238-1
PII:
S 0002-9939(09)10238-1
Keywords:
Loop space,
cobar construction,
strong deformation retract,
acyclic models
Received by editor(s):
March 13, 2009
Posted:
December 21, 2009
Communicated by:
Brooke Shipley
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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