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On decompositions in homotopy theory


Author: Brayton Gray
Journal: Trans. Amer. Math. Soc. 358 (2006), 3305-3328
MSC (2000): Primary 55P35; Secondary 55P30, 55P45
DOI: https://doi.org/10.1090/S0002-9947-05-03964-4
Published electronically: December 20, 2005
MathSciNet review: 2218977
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Abstract: We first describe Krull-Schmidt theorems decomposing $ H$ spaces and simply-connected co-$ H$ spaces into atomic factors in the category of pointed nilpotent $ p$-complete spaces of finite type. We use this to construct a 1-1 correspondence between homotopy types of atomic $ H$ spaces and homotopy types of atomic co-$ H$ spaces, and construct a split fibration which connects them and illuminates the decomposition. Various properties of these constructions are analyzed.


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Additional Information

Brayton Gray
Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045
Email: brayton@uic.edu

DOI: https://doi.org/10.1090/S0002-9947-05-03964-4
Received by editor(s): February 5, 2004
Published electronically: December 20, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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