Homology, Homotopy and Applications

Volume 13 (2011)

Number 2

On the $K$-theory and homotopy theory of the Klein bottle group

Pages: 63 – 72

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n2.a5


Jens Harlander (Mathematics Department, Boise State University, Boise, Idaho, U.S.A.)

Andrew Misseldine (Mathematics Department, Brigham Young University, Provo, Utah, U.S.A.)


We construct infinitely many chain homotopically distinct algebraic 2-complexes for the Klein bottle group and give various topological applications. We compare our examples to other examples in the literature and address the question of geometric realizability.


2-complex; algebraic 2-complex; chain complex; stably free module; relation module; geometric realization

2010 Mathematics Subject Classification

18G35, 20C07, 57M05, 57M20

Published 25 January 2012