Minimal atomic complexes

Baker, A.J. and May, J.P. (2004) Minimal atomic complexes. Topology, 43(3), pp. 645-665. (doi: 10.1016/j.top.2003.09.004)

Abstract

We define <I>minimal atomic complexes</I> and <I>irreducible complexes</I>, and we prove that they are the same. The irreducible complexes admit homological characterizations that make them easy to recognize. These concepts apply both to spaces and to spectra. On the spectrum level, our characterizations allow us to show that such familiar spectra as <I>ko</I>, <I>eo</I><SUB>2</SUB>, and <I>BoP</I> at the prime 2, all <I>BP</I><<I>n</I>> at any prime <I>p</I>, and the indecomposable wedge summands of <IMG height="13" alt="Image" src="http://eprints.gla.ac.uk/images/sigmacp.gif" width="51" align="absBottom" border="0" /> and <IMG height="13" alt="Image" src="http://eprints.gla.ac.uk/images/sigmahp.gif" width="53" align="absBottom" border="0" /> at any prime <I>p</I> are irreducible and therefore minimal atomic. Up to equivalence, the minimal atomic complexes admit escriptions as CW complexes with restricted attaching maps, called <I>nuclear complexes</I>, and this description can be refined further to <I>nuclear minimal complexes</I>, which are nuclear and have zero differential on their mod <I>p</I> chains. As an illustrative example, we construct <I>BoP</I> as a nuclear complex.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Baker, Dr Andrew
• Authors: Baker, A.J., and May, J.P.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Topology
• ISSN: 0040-9383

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