Injective maps between flip graphs

Javier Aramayona; Thomas Koberda; Hugo Parlier

Injective maps between flip graphs

Geometric Topology 2014-12-01 v2 Group Theory

Authors: Javier Aramayona , Thomas Koberda , Hugo Parlier

Abstract

We prove that every injective simplicial map $\mathcal{F}(S) \to \mathcal{F}(S')$ between flip graphs is induced by a subsurface inclusion $S\to S'$ , except in finitely many cases. This extends a result of Korkmaz--Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is induced by a surface homeomorphism.

Cite

@article{arxiv.1409.7046,
  title  = {Injective maps between flip graphs},
  author = {Javier Aramayona and Thomas Koberda and Hugo Parlier},
  journal= {arXiv preprint arXiv:1409.7046},
  year   = {2014}
}

Comments

16 pages, 15 figures. To appear in Ann. Inst. Fourier

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