An exotic presentation of Q_28

Abstract

We introduce a new family of presentations for the quaternion groups and show that for the quaternion group of order 28, one of these presentations has non-standard second homotopy group.

arXiv comment22 pages. Appendix added this version contains proofs of number theoretic results, which make article self-contained

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• Connected sum decompositions of high-dimensional manifolds
• On CW-complexes over groups with periodic cohomology
• Projective modules and the homotopy classification of $(G,n)$-complexes
• Cancellation for $(G,n)$-complexes and the Swan finiteness obstruction
• A fake Klein bottle with bubble