English

Handle decompositions and stabilizations of open books

Geometric Topology 2025-05-27 v1

Abstract

We build handle decompositions of n-manifolds that encode given open book decompositions and describe handle slides that reveal new open book decompositions on the same underlying manifold, for n3n \geq 3. This recovers known stabilization operations for open books. As an application, we show that any open book with trivial monodromy can be stabilized to an open book whose page is a boundary connected sum of trivial disk bundles over spheres.

Keywords

Cite

@article{arxiv.2505.19343,
  title  = {Handle decompositions and stabilizations of open books},
  author = {Chun-Sheng Hsueh},
  journal= {arXiv preprint arXiv:2505.19343},
  year   = {2025}
}

Comments

19 pages, 10 figures