Homology, Homotopy and Applications

The complex of words and Nakaoka stability

Moritz C. Kerz

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Abstract

We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in "general position".

Article information

Source
Homology Homotopy Appl., Volume 7, Number 1 (2005), 77-85.

Dates
First available in Project Euclid: 13 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1139839507

Mathematical Reviews number (MathSciNet)
MR2155519

Zentralblatt MATH identifier
1090.18009

Subjects
Primary: 18G35: Chain complexes [See also 18E30, 55U15]
Secondary: 20J06: Cohomology of groups

Citation

Kerz, Moritz C. The complex of words and Nakaoka stability. Homology Homotopy Appl. 7 (2005), no. 1, 77--85. https://projecteuclid.org/euclid.hha/1139839507


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