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The rank filtration via
a filtered bar construction
Gregory Arone and Kathryn Lesh |
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Algebraic & Geometric Topology 22 (2022) 251–306
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Abstract |
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Suppose is a special –space equipped with a natural transformation . Segal’s infinite loop space machine (Topology 13 (1974) 293–312) associates with a spectrum, denoted by , equipped with a map . In our previous work (Fund. Math. 207 (2010) 29–70), we constructed a filtration of by a sequence of spectra, which we called the stable rank filtration of . Here we give a new construction of the stable rank filtration. The new construction is combinatorial in nature and avoids the process of stabilization. In particular, we construct a sequence of special –spaces whose group completion yields the stable rank filtration. |
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Keywords
$\Gamma$–space, rank filtration, bar construction
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Mathematical Subject Classification 2010
Primary: 55P47
Secondary: 55N15, 55P42
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References |
Publication
Received: 22 March 2020
Revised: 6 January 2021
Accepted: 12 February 2021
Published: 26 April 2022
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Authors |
| Gregory Arone | |
| Department of Mathematics Stockholm University Stockholm Sweden |
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| Kathryn Lesh | |
| Department of Mathematics Union College Schenectady, NY United States |
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| http://www.math.union.edu/~leshk | |
