English

A Generalized Axis Theorem for Cube Complexes

Group Theory 2018-03-16 v2

Abstract

We consider a finitely generated virtually abelian group GG acting properly and without inversions on a CAT(0) cube complex XX. We prove that GG stabilizes a finite dimensional CAT(0) subcomplex YXY \subseteq X that is isometrically embedded in the combinatorial metric. Moreover, we show that YY is a product of finitely many quasilines. The result represents a higher dimensional generalization of Haglund's axis theorem.

Keywords

Cite

@article{arxiv.1602.01952,
  title  = {A Generalized Axis Theorem for Cube Complexes},
  author = {Daniel J. Woodhouse},
  journal= {arXiv preprint arXiv:1602.01952},
  year   = {2018}
}

Comments

14 pages Corrected proof of Corollary 1.4. Various other corrections made following referee report and comments made by thesis examiner. Appendix added giving a proof of a theorem by Gerasimov

R2 v1 2026-06-22T12:44:07.666Z