Homology, Homotopy and Applications

Volume 7 (2005)

Number 1

The complex of words and Nakaoka stability

Pages: 77 – 85

DOI: https://dx.doi.org/10.4310/HHA.2005.v7.n1.a5


Moritz C. Kerz (Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Germany)


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”.


complex of words, homology stability

2010 Mathematics Subject Classification

18G35, 20J06

Published 1 January 2005