English

Special moves for open book decompositions of 3-manifolds

Geometric Topology 2018-01-08 v1

Abstract

We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer's twisting, which is presented in two different (but stably equivalent) forms. Our approach relies on 4-dimensional Lefschetz fibrations, and on 3-dimensional contact topology, via the Giroux-Goodman stable equivalence theorem for open book decompositions representing homologous contact structures.

Keywords

Cite

@article{arxiv.1801.01858,
  title  = {Special moves for open book decompositions of 3-manifolds},
  author = {Riccardo Piergallini and Daniele Zuddas},
  journal= {arXiv preprint arXiv:1801.01858},
  year   = {2018}
}

Comments

16 pages, 11 figures